Merge draft V1 into main, remove build artifacts, update gitignore

- Add assume-guarantee compositional verification citation (Lunze, Alur)
- Address FRET liveness limitation: redirect to continuous mode reachability
- Replace placeholder text with full reactive synthesis → code pipeline
  (Strix, GR(1) fragment, Mealy machines, scalability argument)
- Address parametric uncertainty gap: SpaceEx + conservative over-approximation
- Add systematic Theta_failure construction process (FMEA → parametric bounds)
- Add ARCADE automated code generation paragraph (Pressburger integration risk)
- New \\addedprose{} command for blue new prose in edit mode

.gitignore

@@ -36,3 +36,15 @@ Thumbs.db
 *.swo
 .vscode/
 .idea/
+*.sty
+.DS_Store
+*.aux
+*.bbl
+*.blg
+*.fdb_latexmk
+*.fls
+*.log
+*.pdf
+*.toc
+*.out
+*.synctex.gz

.latexmkrc

@@ -0,0 +1,3 @@
+$pdflatex = 'pdflatex -interaction=nonstopmode %O %S';
+$bibtex_use = 2;
+$pdf_mode = 1;

1-goals-and-outcomes/goals.tex

@@ -16,16 +16,15 @@ manage reactor control. These operators make critical decisions about when to
 switch between different control modes based on their interpretation of plant
 conditions and procedural guidance.
 % Gap
-This reliance on human operators not only prevents autonomous control
-capabilities but creates a fundamental economic challenge for next-generation
-reactor designs. Small modular reactors, in particular, face per-megawatt
-staffing costs far exceeding those of conventional plants and threaten their
-economic viability.
+This reliance on human operators prevents autonomous control and creates a
+fundamental economic barrier for next-generation reactor designs. Small modular
+reactors face per-megawatt staffing costs far exceeding those of conventional
+plants, threatening their economic viability.
 
 % Critical Need
-Autonomous control systems must safely manage complex operational sequences with
-the same assurance as human-operated systems, but without constant human
-supervision.
+What is needed is a method to create autonomous control systems that safely
+manage complex operational sequences with the same assurance as human-operated
+systems, but without constant human supervision.
 % APPROACH PARAGRAPH Solution
 To address this need, we will combine formal methods with control theory to
 build hybrid control systems that are correct by construction.
@@ -35,11 +34,7 @@ mirroring how operators change control strategies. Existing formal methods can
 generate provably correct switching logic from written requirements, but they
 cannot handle the continuous dynamics that occur during transitions between
 modes. Meanwhile, traditional control theory can verify continuous behavior but
-lacks tools for proving correctness of discrete switching
-decisions. This work is conducted within the University of Pittsburgh Cyber Energy Center,
-which provides access to industry collaboration and Emerson control hardware,
-ensuring that developed solutions align with practical implementation
-requirements.
+lacks tools for proving correctness of discrete switching decisions.
 % Hypothesis
 By synthesizing discrete mode transitions directly from written operating
 procedures and verifying continuous behavior between transitions, we can create
@@ -49,7 +44,10 @@ verified against transition requirements, then autonomous controllers can be
 built that are provably free from design defects.
 % Pay-off
 This approach will enable autonomous control in nuclear power plants while
-maintaining the high safety standards required by the industry.
+maintaining the high safety standards required by the industry. The University
+of Pittsburgh Cyber Energy Center's partnership with Emerson provides access to
+industry-standard control hardware, ensuring that developed solutions align with
+practical implementation requirements from the outset.
 
 % OUTCOMES PARAGRAPHS
 If this research is successful, we will be able to do the following:
@@ -66,19 +64,20 @@ If this research is successful, we will be able to do the following:
     logic.
     % Outcome
     Control system engineers will generate verified mode-switching controllers
-    directly from regulatory procedures without formal methods expertise,
-    lowering the barrier to high-assurance control systems.
+    directly from regulatory procedures, lowering the barrier to high-assurance
+    control systems.
 
     % OUTCOME 2 Title
   \item \textbf{Verify continuous control behavior across mode transitions.}
     % Strategy
     We will establish methods for analyzing continuous control modes to ensure
     they satisfy discrete transition requirements. Using classical control
-    theory for linear systems and reachability analysis for nonlinear dynamics,
-    we will verify that each continuous mode safely reaches its intended
-    transitions.
-    Engineers will design continuous controllers using standard practices while
-    iterating to ensure broader system correctness, proving that mode
+    theory for linear systems and reachability analysis for nonlinear
+    dynamics, we will verify that each continuous mode safely reaches its
+    intended transitions.
+    % Outcome
+    Engineers will design continuous controllers using standard practices
+    while iterating to ensure broader system correctness, proving that mode
     transitions occur safely and at the correct times.
 
     % OUTCOME 3  Title
@@ -93,23 +92,18 @@ If this research is successful, we will be able to do the following:
     operation.
     % Outcome
     We will demonstrate that autonomous hybrid control can be realized in the
-    nuclear industry with current equipment, establishing a path toward reduced
-    operator staffing while maintaining safety.
+    nuclear industry with current equipment, establishing a path toward
+    reduced operator staffing while maintaining safety.
 
 \end{enumerate}
 
 % IMPACT PARAGRAPH Innovation
 The innovation in this work is unifying discrete synthesis with continuous
-verification to enable end-to-end correctness guarantees for hybrid 
-systems.
+verification to enable end-to-end correctness guarantees for hybrid systems.
 % Outcome Impact
 If successful, control engineers will create autonomous controllers from
 existing procedures with mathematical proof of correct behavior. High-assurance
 autonomous control will become practical for safety-critical applications.
 % Impact/Pay-off
-This capability is essential for the economic viability of next-generation
-nuclear power. Small modular reactors offer a promising solution to growing
-energy demands, but their success depends on reducing per-megawatt operating
-costs through increased autonomy. This research will provide the tools to
-achieve that autonomy while maintaining the exceptional safety record the
-nuclear industry requires.
+This research will provide the tools to achieve that autonomy while maintaining
+the exceptional safety record the nuclear industry requires.

1-goals-and-outcomes/research-statement.tex

@@ -1,64 +1,57 @@
+\dasnote{Research statement is very similar to GO because that's what I had
+when I prepared it. If it's going to be an executive summary, it should talk
+more about the other sections rather than just being a slightly different GO
+section.}
 % GOAL PARAGRAPH
 The goal of this research is to develop a methodology for creating autonomous
-control systems with event-driven control laws that have guarantees of safe and
-correct behavior.\splitnote{Strong, direct opening. Sets scope immediately.}
+hybrid control systems with mathematical guarantees of safe and correct
+behavior.
 
 % INTRODUCTORY PARAGRAPH Hook
 Nuclear power relies on extensively trained operators who follow detailed
 written procedures to manage reactor control. Based on these procedures and
-operators' interpretation of plant conditions, operators make critical decisions
-about when to switch between control objectives.\splitsuggest{Consider: 
-``operators'' appears 3x in two sentences. Maybe: ``Based on these procedures 
-and their interpretation of plant conditions, they make critical decisions...''}
+their interpretation of plant conditions, they make critical decisions about
+when to switch between control objectives.
 % Gap
-But, reliance on human operators has created an economic challenge for
-next-generation nuclear power plants.\splitpolish{``But, reliance'' — the comma 
-after ``But'' is unusual. Either drop it or restructure: ``However, this 
-reliance...'' or ``This reliance, however, has created...''} Small modular 
-reactors face significantly higher per-megawatt staffing costs than conventional 
-plants. Autonomous control systems are needed that can safely manage complex 
-operational sequences with the same assurance as human-operated systems, but 
-without constant supervision.\splitsuggest{``are needed that can'' — passive. 
-Try: ``Autonomous control systems must safely manage...''}
+This reliance on human operators has created an economic challenge for
+next-generation nuclear power plants. Small modular reactors face significantly
+higher per-megawatt staffing costs than conventional plants. Autonomous control
+systems are needed that can safely manage complex operational sequences with the
+same assurance as human-operated systems, but without constant supervision.
 
 % APPROACH PARAGRAPH Solution
-To address this need, we will combine formal methods from computer science with
-control theory to build hybrid control systems that are correct by 
-construction.\splitnote{Clear statement of approach.}
+To address this need, we will combine formal methods from computer science
+with control theory to build hybrid control systems that are correct by
+construction, leveraging the extensive domain knowledge already embedded in
+existing operating procedures and safety analyses.
 % Rationale
 Hybrid systems use discrete logic to switch between continuous control modes,
 similar to how operators change control strategies. Existing formal methods
-generate provably correct switching logic but cannot handle continuous dynamics
-during transitions, while traditional control theory verifies continuous
-behavior but lacks tools for proving discrete switching 
-correctness.\splitnote{Nice parallel structure showing the gap.}
+generate provably correct switching logic but cannot handle continuous
+dynamics during transitions, while traditional control theory verifies
+continuous behavior but lacks tools for proving discrete switching
+correctness.
+
 % Hypothesis and Technical Approach
 We will bridge this gap through a three-stage methodology. First, we will
 translate written operating procedures into temporal logic specifications using
-NASA's Formal Requirements Elicitation Tool (FRET), which structures
-requirements into scope, condition, component, timing, and response elements.
-This structured approach enables realizability checking to identify conflicts
-and ambiguities in procedures before implementation. Second, we will synthesize
-discrete mode switching logic using reactive synthesis
-to generate deterministic automata that are provably
-correct by construction. Third, we will develop continuous
-controllers for each discrete mode using standard control theory and
-reachability analysis. We will classify continuous modes based on their
-transition objectives, and then employ assume-guarantee contracts and barrier
-certificates to prove that mode transitions occur safely and as defined by the
-deterministic automata. This compositional approach enables local verification
-of continuous modes without requiring global trajectory analysis across the
-entire hybrid system. We will demonstrate this on an Emerson Ovation control 
-system.\splitsuggest{This paragraph is dense. Consider breaking after the 
-three stages, then a new paragraph for the compositional verification point 
-and Emerson demo.}
+NASA's Formal Requirements Elicitation Tool (FRET). FRET structures requirements
+into scope, condition, component, timing, and response elements. This approach
+enables realizability checking that identifies conflicts and ambiguities in
+procedures before implementation. Second, we will synthesize discrete mode
+switching logic using reactive synthesis to produce deterministic automata that
+are correct by construction. Third, we will develop continuous controllers for
+each discrete mode using standard control theory and reachability analysis. We
+will classify continuous modes based on their transition objectives and verify
+safe mode transitions using barrier certificates and reachability analysis.
+This compositional approach enables local verification of continuous modes
+without requiring global trajectory analysis across the entire hybrid system.
+We will validate this methodology through hardware-in-the-loop testing
+on an Emerson Ovation distributed control system, made possible through the
+University of Pittsburgh Cyber Energy Center's industry partnership.
 % Pay-off
-This approach will demonstrate autonomous control can be used for complex
-nuclear power operations while maintaining safety 
-guarantees.\splitpolish{``can be used for'' — weak. Try: ``...will demonstrate 
-that autonomous control can manage complex nuclear power operations while 
-maintaining safety guarantees.'' Or even stronger: ``...enables autonomous 
-management of complex nuclear power operations with safety guarantees.''}
+This approach enables autonomous management of complex nuclear power operations
+while maintaining safety guarantees.
 
 % OUTCOMES PARAGRAPHS
 If this research is successful, we will be able to do the following:
@@ -70,13 +63,11 @@ If this research is successful, we will be able to do the following:
     into formal specifications. These specifications will be synthesized into
     discrete control logic using reactive synthesis tools.
     % Outcome
-    Control engineers will be able to generate mode-switching controllers from
-    regulatory procedures with little formal methods expertise, reducing
-    barriers to high-assurance control 
-    systems.\splitnote{Good practical framing — emphasizes accessibility.}
+    Control engineers will be able to generate mode-switching
+    controllers from regulatory procedures, reducing barriers to high-assurance control systems.
 
     % OUTCOME 2 Title
-  \item \textit{Verify continuous control behavior across mode transitions. }
+  \item \textit{Verify continuous control behavior across mode transitions.}
     % Strategy
     We will develop methods using reachability analysis to ensure continuous
     control modes satisfy discrete transition requirements.
@@ -87,14 +78,13 @@ If this research is successful, we will be able to do the following:
 
     % OUTCOME 3  Title
   \item \textit{Demonstrate autonomous reactor startup control with safety
-    guarantees. }
+    guarantees.}
     % Strategy
     We will implement this methodology on a small modular reactor simulation
-    using industry-standard control hardware.     % Outcome
-    Control engineers will be able to implement high-assurance autonomous
-    controls on industrial platforms they already use, enabling users to
-    achieve autonomy without retraining costs or developing new 
-    equipment.\splitnote{Strong industrial grounding — the ``platforms they 
-    already use'' point is compelling for adoption.}
+    using industry-standard control hardware.
+    % Outcome
+    Without retraining costs or new equipment, control engineers
+    will be able to implement high-assurance autonomous controls on industrial
+    hardware they already use. 
 
 \end{enumerate}

2-state-of-the-art/state-of-art.tex

@@ -1,149 +1,130 @@
 \section{State of the Art and Limits of Current Practice}
 
 The principal aim of this research is to create autonomous reactor control
-systems that are tractably safe. To understand what is being automated, we must
-first understand how nuclear reactors are operated today. This section examines
-reactor operators and the operating procedures we aim to leverage, then
-investigates limitations of human-based operation, and concludes with current
-formal methods approaches to reactor control 
-systems.
+systems that are tractably safe. Understanding what is being automated requires
+understanding how nuclear reactors are operated today. This section examines
+reactor operating procedures, investigates limitations of human-based operation,
+and reviews current formal methods approaches to reactor control systems.
 
 \subsection{Current Reactor Procedures and Operation}
 
-Nuclear plant procedures exist in a hierarchy: normal operating procedures for
-routine operations, abnormal operating procedures for off-normal conditions,
-Emergency Operating Procedures (EOPs) for design-basis accidents, Severe
-Accident Management Guidelines (SAMGs) for beyond-design-basis events, and
-Extensive Damage Mitigation Guidelines (EDMGs) for catastrophic damage
-scenarios. These procedures must comply with 10 CFR 50.34(b)(6)(ii) and are
-developed using guidance from NUREG-0899~\cite{NUREG-0899, 10CFR50.34}, but their
-development relies fundamentally on expert judgment and simulator validation
-rather than formal verification. Procedures undergo technical evaluation,
-simulator validation testing, and biennial review as part of operator
-requalification under 10 CFR 55.59~\cite{10CFR55.59}. 
+Nuclear plant operations are governed by a hierarchy of written procedures,
+ranging from normal operating procedures for routine operations to Emergency
+Operating Procedures (EOPs) for design-basis accidents and Severe Accident
+Management Guidelines (SAMGs) for beyond-design-basis events. These procedures
+exist because reactor operation requires deterministic responses to a wide range
+of plant conditions, from routine power changes to catastrophic failures. These
+procedures must comply with 10 CFR 50.34(b)(6)(ii) and are developed using
+guidance from NUREG-0899~\cite{NUREG-0899, 10CFR50.34}. Procedures undergo
+technical evaluation, simulator validation testing, and biennial review as part
+of operator requalification under 10 CFR 55.59~\cite{10CFR55.59}. Despite this
+rigor, procedures fundamentally lack exhaustive verification of key safety
+properties. 
 
-\textbf{LIMITATION:} \textit{Procedures lack formal verification of correctness
-and completeness.} Current procedure development relies on expert judgment and
-simulator validation. No mathematical proof exists that procedures cover all
-possible plant states, that required actions can be completed within available
-timeframes, or that transitions between procedure sets maintain safety
+\textbf{LIMITATION:} \textit{Procedures lack exhaustive verification of
+correctness and completeness.}  No mathematical proof exists that procedures
+cover all possible plant states, that required actions can be completed within
+available timeframes, or that transitions between procedure sets maintain safety
 invariants. Paper-based procedures cannot ensure correct application, and even
 computer-based procedure systems lack the formal guarantees that automated
 reasoning could provide.
 
-Nuclear plants operate with multiple control modes: automatic control, where the
-reactor control system maintains target parameters through continuous reactivity
-adjustment; manual control, where operators directly manipulate the reactor; and
-various intermediate modes. In typical pressurized water reactor operation, the
-reactor control system automatically maintains a floating average temperature
-and compensates for power demand changes through reactivity feedback loops
-alone. Safety systems, by contrast, operate with implemented automation. Reactor
-Protection Systems trip automatically on safety signals with millisecond
-response times, and engineered safety features actuate automatically on accident
-signals without operator action required.
+Nuclear plants operate with multiple control modes: automatic control, where
+the reactor control system maintains target parameters through continuous
+reactivity adjustment; manual control, where operators directly manipulate
+the reactor; and various intermediate modes. In typical pressurized water
+reactor operation, the reactor control system automatically maintains a
+floating average temperature and compensates for power demand changes through
+reactivity feedback loops alone. Safety systems, by contrast, operate with
+implemented automation. Reactor Protection Systems trip automatically on
+safety signals with millisecond response times, and engineered safety
+features actuate automatically on accident signals without operator action
+required.
 
-The division between automated and human-controlled functions reveals the
-fundamental challenge of hybrid control. Highly automated systems handle reactor
-protection---automatic trips on safety parameters, emergency core cooling
+This division between automated and human-controlled
+functions is itself the hybrid control problem. Automated systems handle
+reactor protection: trips on safety parameters, emergency core cooling
 actuation, containment isolation, and basic process
-control~\cite{WRPS.Description, gentillon_westinghouse_1999}. Human operators,
-however, retain control of strategic decision-making: power level changes,
+control~\cite{WRPS.Description, gentillon_westinghouse_1999}. Human
+operators retain control of everything else: power level changes,
 startup/shutdown sequences, mode transitions, and procedure
 implementation.
 
-\subsection{Human Factors in Nuclear Accidents}
-
-Current-generation nuclear power plants employ over 3,600 active NRC-licensed
-reactor operators in the United States~\cite{operator_statistics}. These
-operators divide into Reactor Operators (ROs), who manipulate reactor controls,
-and Senior Reactor Operators (SROs), who direct plant operations and serve as
-shift supervisors~\cite{10CFR55}. Staffing typically requires at least two ROs
-and one SRO for current-generation units~\cite{10CFR50.54}. Becoming a reactor
-operator requires several years of training.
-
 The persistent role of human error in nuclear safety incidents---despite decades
 of improvements in training and procedures---provides the most compelling
-motivation for formal automated control with mathematical safety 
-guarantees. Operators hold legal authority under 10 CFR Part 55 to make critical decisions,
-including departing from normal regulations during emergencies. The Three Mile
-Island (TMI) accident demonstrated how a combination of personnel error, design
-deficiencies, and component failures led to partial meltdown when operators
-misread confusing and contradictory readings and shut off the emergency water
+motivation for formal automated control with mathematical safety guarantees.
+Operators hold legal authority under 10 CFR Part 55 to make critical
+decisions~\cite{10CFR55}, including departing from normal regulations during
+emergencies. This authority itself introduces risk. The Three Mile Island (TMI)
+accident demonstrated how a combination of personnel error, design deficiencies,
+and component failures led to partial meltdown when operators misread confusing
+and contradictory readings and shut off the emergency water
 system~\cite{Kemeny1979}. The President's Commission on TMI identified a
 fundamental ambiguity: placing responsibility for safe power plant operations on
 the licensee without formal verification that operators can fulfill this
 responsibility does not guarantee safety. This tension between operational
 flexibility and safety assurance remains unresolved: the person responsible for
-reactor safety is often the root cause of 
-failures.
+reactor safety is often the root cause of failures.
 
 Multiple independent analyses converge on a striking statistic: 70--80\% of
 nuclear power plant events are attributed to human error, versus approximately
-20\% to equipment failures~\cite{WNA2020}. More significantly, the root cause of
-all severe accidents at nuclear power plants---Three Mile Island, Chernobyl, and
-Fukushima Daiichi---has been identified as poor safety management and safety
-culture: primarily human factors~\cite{hogberg_root_2013}. A detailed analysis
-of 190 events at Chinese nuclear power plants from
-2007--2020~\cite{zhang_analysis_2025} found that 53\% of events involved active
-errors, while 92\% were associated with latent errors---organizational and
-systemic weaknesses that create conditions for 
+20\% to equipment failures~\cite{noauthor_human_nodate}. More significantly, the
+root cause of all severe accidents at nuclear power plants---Three Mile Island,
+Chernobyl, and Fukushima Daiichi---has been identified as primarily human
+factors~\cite{hogberg_root_2013}. A detailed analysis of 190 events at Chinese
+nuclear power plants from 2007--2020~\cite{zhang_analysis_2025} found that 53\%
+of events involved active errors, while 92\% were associated with latent
+errors---organizational and systemic weaknesses that create conditions for
 failure.
 
-
-\textbf{LIMITATION:} \textit{Human factors impose fundamental reliability limits
-that cannot be overcome through training alone.} The persistent human
-error contribution despite four decades of improvements demonstrates that these
-limitations are fundamental rather than a remediable part of human-driven 
-control.
+\textbf{LIMITATION:} \textit{Human factors impose fundamental reliability
+limits that cannot be overcome through training alone.} The persistent human
+error contribution despite four decades of improvements demonstrates that
+these limitations are fundamental rather than a remediable part of
+human-driven control.
 
 \subsection{Formal Methods}
 \subsubsection{HARDENS}
 
 The High Assurance Rigorous Digital Engineering for Nuclear Safety (HARDENS)
 project represents the most advanced application of formal methods to nuclear
-reactor control systems to date~\cite{Kiniry2024}.
+reactor control systems to date~\cite{Kiniry2024}. HARDENS aimed to address a
+fundamental dilemma: existing U.S. nuclear control rooms rely on analog
+technologies from the 1950s--60s. This technology is obsolete compared to modern
+control systems and incurs significant risk and cost. A U.S. Nuclear Regulatory
+Commission report demonstrated that model-based systems engineering and formal
+methods could design, verify, and implement a complex protection system meeting
+regulatory criteria. The project delivered a Reactor Trip System (RTS)
+implementation with traceability from regulatory requirements to verified
+software through formal architecture specifications.
 
-HARDENS aimed to address a fundamental dilemma: existing U.S. nuclear control
-rooms rely on analog technologies from the 1950s--60s. This technology is
-obsolete compared to modern control systems and incurs significant risk and
-cost. The NRC contracted Galois, a formal methods firm, to demonstrate that
-Model-Based Systems Engineering and formal methods could design, verify, and
-implement a complex protection system meeting regulatory criteria at a fraction
-of typical cost. The project delivered a Reactor Trip System (RTS)
-implementation with full traceability from NRC Request for Proposals and IEEE
-standards through formal architecture specifications to verified software.
-
-HARDENS employed formal methods tools and techniques across the verification
-hierarchy. High-level specifications used Lando, SysMLv2, and FRET (NASA Formal
-Requirements Elicitation Tool) to capture stakeholder requirements, domain
-engineering, certification requirements, and safety requirements. Requirements
-were analyzed for consistency, completeness, and realizability using SAT and SMT
-solvers. Executable formal models used Cryptol to create a behavioral model of
-the entire RTS, including all subsystems, components, and limited digital twin
-models of sensors, actuators, and compute infrastructure. Automatic code
-synthesis generated verifiable C implementations and SystemVerilog hardware
+HARDENS employed formal methods tools at every level of system development, from
+high-level requirements through executable models to generated code. High-level
+specifications used Lando, SysMLv2, and FRET (NASA Formal Requirements
+Elicitation Tool) to capture stakeholder requirements, domain engineering,
+certification requirements, and safety requirements. Requirements were analyzed
+for consistency, completeness, and realizability using SAT and SMT solvers.
+Executable formal models used Cryptol to create a behavioral model of the entire
+RTS, including all subsystems, components, and limited digital twin models of
+sensors, actuators, and compute infrastructure. Automatic code synthesis
+generated verifiable C implementations and SystemVerilog hardware
 implementations directly from Cryptol models---eliminating the traditional gap
-between specification and implementation where errors commonly 
-arise.
+between specification and implementation where errors commonly arise.
 
-Despite its accomplishments, HARDENS has a fundamental limitation directly
-relevant to hybrid control synthesis: the project addressed only discrete
-digital control logic without modeling or verifying continuous reactor dynamics.
-The Reactor Trip System specification and verification covered discrete state
-transitions (trip/no-trip decisions), digital sensor input processing through
-discrete logic, and discrete actuation outputs (reactor trip commands). The
-project did not address continuous dynamics of nuclear reactor physics. Real
-reactor safety depends on the interaction between continuous
-processes---temperature, pressure, neutron flux---evolving in response to
-discrete control decisions. HARDENS verified the discrete controller in
-isolation but not the closed-loop hybrid system 
-behavior.
+Despite these accomplishments, HARDENS addressed only discrete digital
+control logic. The Reactor Trip System verification covered discrete state
+transitions, digital sensor processing, and discrete actuation outputs. It
+did not model or verify continuous reactor dynamics. Real reactor safety
+depends on the interaction between continuous processes---temperature,
+pressure, neutron flux---evolving in response to discrete control decisions.
+HARDENS verified the discrete controller in isolation but not a
+closed-loop hybrid system behavior.
 
-\textbf{LIMITATION:} \textit{HARDENS addressed discrete control logic without
-continuous dynamics or hybrid system verification.} Verifying discrete control
-logic alone provides no guarantee that the closed-loop system exhibits desired
-continuous behavior such as stability, convergence to setpoints, or maintained
-safety margins.
+\textbf{LIMITATION:} \textit{HARDENS addressed discrete control logic
+without continuous dynamics or hybrid system verification.} Verifying
+discrete control logic alone provides no guarantee that the closed-loop
+system exhibits desired continuous behavior such as stability, convergence to
+setpoints, or maintained safety margins.
 
 HARDENS produced a demonstrator system at Technology Readiness Level 2--3
 (analytical proof of concept with laboratory breadboard validation) rather than
@@ -153,59 +134,83 @@ considered in development, not a finalized product, and that ``The demonstration
 of its technical soundness was to be at a level consistent with satisfaction of
 the current regulatory criteria, although with no explicit demonstration of how
 regulatory requirements are met.'' The project did not include deployment in
+%DAS 3/16/26. I double checked this quote. It's on page 4 of the HARDENS report
 actual nuclear facilities, testing with real reactor systems under operational
 conditions, side-by-side validation with operational analog RTS systems,
-systematic failure mode testing (radiation effects, electromagnetic
-interference, temperature extremes), NRC licensing review, or human factors
+systematic failure mode testing, NRC licensing review, or human factors
 validation with licensed operators in realistic control room scenarios.
 
 \textbf{LIMITATION:} \textit{HARDENS achieved TRL 2--3 without experimental
 validation.} While formal verification provides mathematical correctness
 guarantees for the implemented discrete logic, the gap between formal
 verification and actual system deployment involves myriad practical
-considerations: integration with legacy systems, long-term reliability
-under harsh environments, human-system interaction in realistic
-operational contexts, and regulatory acceptance of formal methods as
-primary assurance evidence.
+considerations: integration with legacy systems, human-system interaction in
+realistic operational contexts, and regulatory acceptance of formal methods as
+primary assurance evidence remain as significant challenges.
 
-\subsubsection{Sequent Calculus and Differential Dynamic Logic}
-There has been additional work to do verification of hybrid systems by extending
-the temporal logics directly. The result has been the field of differential
-dynamic logic (dL). dL introduces two additional operators
-into temporal logic: the box operator and the diamond operator. The box operator
-\([\alpha]\phi\) states that for some region \(\phi\), the hybrid system
-\(\alpha\) always remains within that region. In this way, it is a safety
-invariant being enforced for the system. The second operator, the diamond
-operator \(<\alpha>\phi\) says that for the region \(\phi\), there is at least
-one trajectory of \(\alpha\) that enters that region. This is a declaration of a
-liveness property\cite{platzer2018}. 
+\subsubsection{Temporal Logic and Formal Specification}
+
+Formal verification of any system requires a precise language for stating
+what the system must do. Temporal logic provides this language by extending
+classical propositional logic with operators that express properties over
+time~\cite{baier_principles_2008}. Where propositional logic can state that
+a condition is true or false, temporal logic can state that a condition must
+always hold, must eventually hold, or must hold until some other condition is
+met. Linear temporal logic (LTL) formalizes these notions through four key
+operators:
+\begin{itemize}
+  \item $\mathbf{X}\phi$ (next): $\phi$ holds in the next state
+  \item $\mathbf{G}\phi$ (globally): $\phi$ holds in all future states
+  \item $\mathbf{F}\phi$ (finally): $\phi$ holds in some future state
+  \item $\phi \mathbf{U} \psi$ (until): $\phi$ holds until $\psi$ becomes
+    true
+\end{itemize}
+These operators allow specification of safety properties ($\mathbf{G}\neg
+\textit{Unsafe}$), liveness properties ($\mathbf{F}\textit{ Target}$), and
+response properties ($\mathbf{G}(\textit{Trigger} \rightarrow
+\mathbf{F}\textit{ Response})$). For nuclear control, this expressiveness
+captures exactly the kinds of requirements that matter: the reactor must
+never enter an unsafe configuration, the system must eventually reach
+operating temperature, and if coolant pressure drops, shutdown must initiate
+within bounded time. These properties can be derived directly from operating
+procedures and regulatory requirements, creating a formal link between
+existing documentation and verifiable system behavior.
+
+\subsubsection{Differential Dynamic Logic}
+
+A separate line of work extends temporal logics to verify hybrid systems
+directly. The result has been the field of differential dynamic logic
+(dL)~\cite{platzer_differential_2008}. dL
+introduces two additional operators into temporal logic: the box operator and
+the diamond operator. The box operator \([\alpha]\phi\) states that for some
+region \(\phi\), the hybrid system \(\alpha\) always remains within that
+region. In this way, it is a safety invariant being
+enforced for the system. The second operator, the diamond operator
+\(<\alpha>\phi\) says that for the region \(\phi\), there is at least one
+trajectory of \(\alpha\) that enters that region. This is a declaration of a
+liveness property.
 
 
 While dL allows for the specification of these liveness and safety properties,
 actually proving them for a given hybrid system is quite difficult. Automated
-proof assistants such as KeYmaera X exist to help develop proofs of systems
+proof assistants such as KeYmaera X~\cite{fulton_keymaera_2015} exist to help
+develop proofs of systems
 using dL, but so far have been insufficient for reasonably complex hybrid
-systems. The main issue behind creating system proofs using dL is state space
-explosion and non-terminating 
-solutions.\splitsuggest{Consider adding a concrete example here — ``For 
-instance, a system with N modes and M continuous state variables...'' to give 
-readers a sense of the scaling problem.}
-%Source: that one satellite tracking paper that has the problem with the
-%gyroscopes overloding and needing to dump speed all the time
-Approaches have been made to alleviate
-these issues for nuclear power contexts using contract and decomposition based
-methods, but do not yet constitute a complete design
-methodology\cite{kapuria2025}.%source: Manyu's thesis. 
+systems. The main issue behind creating system proofs using dL is
+non-terminating solutions. Approaches have been made to alleviate these issues
+for nuclear power contexts using contract and decomposition based methods, but
+do not yet constitute a complete design methodology \cite{kapuria_using_2025}.
 Instead, these approaches have been used on systems that have been designed a
 priori, and require expert knowledge to create the system proofs.
 
 %Maybe a limitation here? Something about dL doesn't scale or help in design
-%very much, so the limitation is that logic based hybrid system approaches have
-%not been used in the DESIGN of autonomous controllers, only in the analysis of
-%systems that already exist.
+%very much, so the limitation is that logic based hybrid system approaches
+%have not been used in the DESIGN of autonomous controllers, only in the
+%analysis of systems that already exist.
+
 \textbf{LIMITATION:} \textit{Differential dynamic logic has been used for
 post-hoc analysis of existing systems, not for the constructive design of
-autonomous controllers.} Current formal methods based approaches can in theory
-completely describe the behavior of a hybrid autonomous control system, but in
-practice remain difficult to implement, and have no straightforward application
-to the design of a hybrid autonomous control system.
+autonomous controllers.} Current dL-based approaches verify systems that
+have already been designed, requiring expert knowledge to construct proofs.
+They have not been applied to the synthesis of new controllers from
+operational requirements.

3-research-approach/approach.tex

@@ -1,87 +1,77 @@
 \section{Research Approach}
 
-% ============================================================================
-% STRUCTURE (maps to Thesis.RA tasks):
-%   1. Introduction + Hybrid Systems Definition (Task 34)
-%   2. System Requirements and Specifications (Task 35)
-%   3. Discrete Controller Synthesis (Task 36)
-%   4. Continuous Controllers Overview (Task 37)
-%      4.1 Transitory Modes (Task 38)
-%      4.2 Stabilizing Modes (Task 39)
-%      4.3 Expulsory Modes (Task 40)
-%   5. Industrial Implementation (Task 41)
-% ============================================================================
-
-% ----------------------------------------------------------------------------
-% 1. INTRODUCTION AND HYBRID SYSTEMS DEFINITION
-% ----------------------------------------------------------------------------
-Previous approaches to autonomous control have verified
-discrete switching logic or continuous control behavior, but not both
-simultaneously. Validation of continuous controllers today consists of
-extensive simulation trials. Discrete switching logic for routine operation
-has been driven by human operators, whose evaluation includes simulated
-control room testing and human factors research. Neither method, despite
-being extremely resource intensive, provides rigorous guarantees of control
-system behavior. HAHACS bridges this gap by composing formal methods from
-computer science with control-theoretic verification, formalizing reactor
-operations using the framework of hybrid automata.
-
-The challenge of hybrid system verification lies in the interaction between
-discrete and continuous dynamics. Discrete transitions change the governing
-vector field, creating discontinuities in the system's behavior. Traditional
-verification techniques designed for purely discrete or purely continuous
-systems cannot handle this interaction directly. Our methodology addresses this
-challenge through decomposition. We verify discrete switching logic and
-continuous mode behavior separately, then compose these guarantees to reason
-about the complete hybrid system. This two-layer approach mirrors the structure
-of reactor operations themselves: discrete supervisory logic determines which
-control mode is active, while continuous controllers govern plant behavior
-within each mode.
-
 To build a high-assurance hybrid autonomous control system (HAHACS), we must
 first establish a mathematical description of the system. This work draws on
 automata theory, temporal logic, and control theory. A hybrid system is a
-dynamical system that has both continuous and discrete states. The specific type
-of system discussed in this proposal is a continuous autonomous hybrid system.
-This means that the system does not have external input and that continuous
-states do not change instantaneously when discrete states change. For our
-systems of interest, the continuous states are physical quantities that are
-always Lipschitz continuous. This nomenclature is borrowed from the Handbook on
-Hybrid Systems Control \cite{lunze2009}, but is redefined here
-for convenience:
-
+dynamical system that has both continuous and discrete states. The specific
+type of system discussed in this proposal is a continuous autonomous hybrid
+system. This means that the system does not have external input and that
+continuous states do not change instantaneously when discrete states change.
+For our systems of interest, the continuous states are physical quantities
+that are always Lipschitz continuous. This nomenclature is borrowed from the
+Handbook on Hybrid Systems Control \cite{lunze_handbook_2009}, but is
+redefined here for convenience:
+%
 \begin{equation}
-  H = (\mathcal{Q}, \mathcal{X}, \mathbf{f}, Init, \mathcal{G}, \delta, \mathcal{R}, Inv)
+  H = (\mathcal{Q}, \mathcal{X}, \mathbf{f}, Init, \mathcal{G}, \delta,
+  \mathcal{R}, Inv)
 \end{equation}
-
+%
 where:
-
+%
 \begin{itemize}
   \item $\mathcal{Q}$: the set of discrete states (modes) of the system
   \item $\mathcal{X} \subseteq \mathbb{R}^n$: the continuous state space
-  \item $\mathbf{f}: \mathcal{Q} \times \mathcal{X} \rightarrow \mathbb{R}^n$:
-    vector fields defining the continuous dynamics for each discrete mode $q_i$
-  \item $Init \subseteq \mathcal{Q} \times \mathcal{X}$: the set of initial states
+  \item $\mathbf{f}: \mathcal{Q} \times \mathcal{X} \rightarrow
+    \mathbb{R}^n$: vector fields defining the continuous dynamics for each
+    discrete mode $q_i$
+  \item $Init \subseteq \mathcal{Q} \times \mathcal{X}$: the set of initial
+    states
   \item $\mathcal{G}$: guard conditions that define when discrete state
     transitions may occur
-  \item $\delta: \mathcal{Q} \times \mathcal{G} \rightarrow \mathcal{Q}$: the
-    discrete state transition function
+  \item $\delta: \mathcal{Q} \times \mathcal{G} \rightarrow \mathcal{Q}$:
+    the discrete state transition function
   \item $\mathcal{R}$: reset maps that define any instantaneous changes to
     continuous state upon discrete transitions
   \item $Inv$: safety invariants on the continuous dynamics
 \end{itemize}
 
-The creation of a HAHACS amounts to the construction of such a tuple together
-with proof artifacts demonstrating that the intended behavior of the control
-system is satisfied by its actual implementation. This approach is tractable now
-because the infrastructure for each component has matured. The novelty is not in
-the individual pieces, but in the architecture that connects them. 
+HAHACS bridges the gap between discrete and continuous verification by composing
+formal methods from computer science with control-theoretic verification,
+formalizing reactor operations using the framework of hybrid
+automata~\cite{alur_hybrid_1993}. The challenge of hybrid system verification
+lies in the interaction between discrete and continuous dynamics. Discrete
+transitions change the active continuous vector field, creating discontinuities
+in the system's behavior. Traditional verification techniques designed for
+purely discrete or purely continuous systems cannot handle this interaction
+directly. Our methodology addresses this challenge through decomposition. We
+verify discrete switching logic and continuous mode behavior separately, then
+compose these guarantees to reason about the complete hybrid system. This
+compositional strategy follows the assume-guarantee paradigm for hybrid systems,
+where guarantees about individual modes compose into guarantees about the
+overall system~\cite{lunze_handbook_2009, alur_hybrid_1993}. This two-layer
+approach mirrors the structure of reactor operations themselves: discrete
+supervisory logic determines which control mode is active, while continuous
+controllers govern plant behavior within each mode.
 
-By defining entry, exit, and safety conditions at the discrete level first, we
-transform the intractable problem of global hybrid verification into a
-collection of local verification problems with clear interfaces. Verification is
-performed per mode rather than on the full hybrid system, keeping the analysis
-tractable even for complex reactor operations.
+The creation of a HAHACS amounts to the construction of such a tuple
+together with proof artifacts demonstrating that the intended behavior of the
+control system is satisfied by its actual
+implementation. In concrete terms, this means producing a
+discrete automaton whose transitions are provably correct, continuous
+controllers whose behavior is verified against transition requirements, and
+formal evidence linking the two. This approach is tractable now because the
+infrastructure for each component has matured. The novelty is not in the
+individual pieces, but in the architecture that connects
+them. By defining entry, exit, and safety conditions at the
+discrete level first, we transform the intractable problem of global hybrid
+verification into a collection of local verification problems with clear
+interfaces. Verification is performed per mode rather than on the full
+hybrid system, keeping the analysis tractable even for complex reactor
+operations. Figure~\ref{fig:hybrid_automaton} illustrates this
+structure for a simplified reactor startup sequence, showing discrete modes
+connected by guard-triggered transitions with continuous dynamics governing
+behavior within each mode.
 
 \begin{figure}
   \centering
@@ -107,58 +97,58 @@ tractable even for complex reactor operations.
     \node[state, fill=red!15] (q3) at (5,-3.5) {$q_3$\\SCRAM};
 
     % Normal transitions
-    \draw[trans] (q0) -- node[guard, above] {$T_{avg} > T_{min}$} (q1);
-    \draw[trans] (q1) -- node[guard, above] {$T_{avg} \in [T_{op} \pm \delta]$\\$P > P_{crit}$} (q2);
+    \draw[trans] (q0) -- node[guard, above]
+      {$T_{avg} > T_{min}$} (q1);
+    \draw[trans] (q1) -- node[guard, above]
+      {$T_{avg} \in [T_{op} \pm \delta]$\\$P > P_{crit}$} (q2);
 
     % Fault transitions
-    \draw[trans, red!70!black] (q1) -- node[guard, left, text=red!70!black] {$\neg Inv_1$} (q3);
-    \draw[trans, red!70!black] (q2) to[bend left=20] node[guard, right, text=red!70!black] {$\neg Inv_2$} (q3);
+    \draw[trans, red!70!black] (q1) -- node[guard, left,
+      text=red!70!black] {$\neg Inv_1$} (q3);
+    \draw[trans, red!70!black] (q2) to[bend left=20] node[guard,
+      right, text=red!70!black] {$\neg Inv_2$} (q3);
 
     % Recovery transition
-    \draw[trans, dashed] (q3) to[bend left=30] node[guard, below] {Manual reset} (q0);
+    \draw[trans, dashed] (q3) to[bend left=30] node[guard, below]
+      {Manual reset} (q0);
 
     % Self-loops indicating staying in mode
-    \draw[trans] (q2) to[loop right] node[guard, right] {$Inv_2$} (q2);
+    \draw[trans] (q2) to[loop right] node[guard, right] {$Inv_2$}
+      (q2);
 
     % Dynamics labels below states
     \node[dynamics] at (0,-1.4) {$\dot{x} = f_0(x)$};
-    \node[dynamics] at (6,-1.2) {$\dot{x} = f_1(x,u)$};
-    \node[dynamics] at (10,-1.4) {$\dot{x} = f_2(x,u)$};
+    \node[dynamics] at (6,-1.2) {$\dot{x} = f_1(x)$};
+    \node[dynamics] at (10,-1.4) {$\dot{x} = f_2(x)$};
     \node[dynamics] at (5,-4.9) {$\dot{x} = f_3(x)$};
 
   \end{tikzpicture}
-  \caption{Simplified hybrid automaton for reactor startup. Each discrete state 
-    $q_i$ has associated continuous dynamics $f_i$. Guard conditions on 
-    transitions (e.g., $T_{avg} > T_{min}$) are predicates over continuous 
-    state. Invariant violations ($\neg Inv_i$) trigger transitions to the 
-    SCRAM state. The operational level manages discrete transitions; the 
-    tactical level executes continuous control within each mode.}
+  \caption{Simplified hybrid automaton for reactor startup. Each discrete
+    state $q_i$ has associated continuous dynamics $f_i$. Guard conditions
+    on transitions (e.g., $T_{avg} > T_{min}$) are predicates over
+    continuous state. Invariant violations ($\neg Inv_i$) trigger
+    transitions to the SCRAM state. The operational level manages discrete
+    transitions; the tactical level executes continuous control within each
+    mode.}
   \label{fig:hybrid_automaton}
 \end{figure}
 
-%%% NOTES (Section 1):
-% - May want to clarify the "no external input" claim with a footnote about
-%   strategic inputs (e.g., remote start/stop commands)
-% - The reset map R is often identity for physical systems; clarify if needed
-
-% ----------------------------------------------------------------------------
-% 2. SYSTEM REQUIREMENTS AND SPECIFICATIONS
-% ----------------------------------------------------------------------------
-
 \subsection{System Requirements, Specifications, and Discrete Controllers}
+
 Human control of nuclear power can be divided into three different scopes:
-strategic, operational, and tactical. Strategic control is high-level and
-long-term decision making for the plant. This level has objectives that are
-complex and economic in scale, such as managing labor needs and supply chains to
-optimize scheduled maintenance and downtime. The time scale at this level is
-long, often spanning months or years. The lowest level of control is the
-tactical level. This is the individual control of pumps, turbines, and
-chemistry. Tactical control has already been somewhat automated in nuclear power
-plants today, and is generally considered ``automatic control'' when autonomous.
-These controls are almost always continuous systems with a direct impact on the
-physical state of the plant. Tactical control objectives include maintaining
-pressurizer level, maintaining core temperature, or adjusting reactivity with a
-chemical shim.
+strategic, operational, and tactical.\footnote{This was inspired by an article
+about battlefield organizational science~\cite{harvey_levels_2021}.} Strategic
+control is high-level and long-term decision making for the plant. This level
+has objectives that are complex and economic in scale, such as managing labor
+needs and supply chains to optimize scheduled maintenance and downtime. The time
+scale at this level is long, often spanning months or years. The lowest level of
+control is the tactical level. This is the individual control of pumps,
+turbines, and chemistry. Tactical control has already been somewhat automated in
+nuclear power plants today, and is generally considered ``automatic control''
+when autonomous. These controls are almost always continuous systems with a
+direct impact on the physical state of the plant. Tactical control objectives
+include, but are not limited to, maintaining pressurizer level, maintaining core
+temperature, or adjusting reactivity with a chemical shim.
 
 The level of control linking these two extremes is the operational control
 scope. Operational control is the primary responsibility of human operators
@@ -168,22 +158,19 @@ way, it bridges high-level and low-level goals. A strategic goal may be to
 perform refueling at a certain time, while the tactical level of the plant is
 currently focused on maintaining a certain core temperature. The operational
 level issues the shutdown procedure, using several smaller tactical goals along
-the way to achieve this objective. Thus, the combination of the operational and
-tactical levels fundamentally forms a hybrid controller. The tactical level is
-the continuous evolution of the plant according to the control input and control
-law, while the operational level is a discrete state evolution that determines
-which tactical control law to apply.
-
-%Say something about autonomous control systems near here?
-
+the way to achieve this strategic objective. This hierarchical division of
+control scope and objectives is illustrated graphically in
+figure~\ref{fig:strat_op_tact}. 
 
 \begin{figure}
   \centering
   \begin{tikzpicture}[scale=0.8]
     % Pyramid layers
     \fill[blue!30!white] (0,4) -- (2,4) -- (1,5.) -- cycle;
-    \fill[blue!20!white] (-1.5,2.5) -- (3.5,2.5) -- (2,4) -- (0,4) -- cycle;
-    \fill[blue!10!white] (-3,1) -- (5,1) -- (3.5,2.5) -- (-1.5,2.5) -- cycle;
+    \fill[blue!20!white] (-1.5,2.5) -- (3.5,2.5) -- (2,4) -- (0,4)
+      -- cycle;
+    \fill[blue!10!white] (-3,1) -- (5,1) -- (3.5,2.5) -- (-1.5,2.5)
+      -- cycle;
 
     % Labels inside pyramid
     \node[font=\small\bfseries] at (1,4.5) {Strategic};
@@ -192,119 +179,132 @@ which tactical control law to apply.
 
     % Descriptions to the right
     \node[anchor=west, font=\small, text width=8cm] at (5.5,4.6)
-      {\textit{Long-term planning:} maintenance scheduling, capacity planning, economic dispatch};
+      {\textit{Long-term planning:} maintenance scheduling, capacity
+      planning, economic dispatch};
     \node[anchor=west, font=\small, text width=8cm] at (5.5,3.1)
-      {\textit{Discrete decisions:} startup/shutdown sequences, power level changes, mode transitions};
+      {\textit{Discrete decisions:} startup/shutdown sequences, power
+      level changes, mode transitions};
     \node[anchor=west, font=\small, text width=8cm] at (5.5,1.6)
-      {\textit{Continuous control:} temperature regulation, pressure control, load following};
+      {\textit{Continuous control:} temperature regulation, pressure
+      control, load following};
 
     % Bracket showing HAHACS scope (simple line with text)
-    \draw[thick] (5.0,1.0) -- (-3.5,1) -- (-3.5,4) -- (2.0,4) -- cycle;
-    \node[font=\small, align=center, rotate=90] at (-4.2,2.5) {HAHACS scope};
+    \draw[thick] (5.0,1.0) -- (-3.5,1) -- (-3.5,4) -- (2.0,4) --
+      cycle;
+    \node[font=\small, align=center, rotate=90] at (-4.2,2.5)
+      {HAHACS scope};
   \end{tikzpicture}
-  \caption{Control scope hierarchy in nuclear power operations. Strategic control 
-    (long-term planning) remains with human management. HAHACS addresses the 
-    operational level (discrete mode switching) and tactical level (continuous 
-    control within modes), which together form a hybrid control system.}
+  \caption{Control scope hierarchy in nuclear power operations.
+    Strategic control (long-term planning) remains with human management.
+    HAHACS addresses the operational level (discrete mode switching) and
+    tactical level (continuous control within modes), which together form
+    a hybrid control system.}
   \label{fig:strat_op_tact}
 \end{figure}
 
-
 This operational control level is the main reason for the requirement of human
 operators in nuclear control today. The hybrid nature of this control system
-makes it difficult to prove that a controller will perform according to
-strategic requirements, as unified infrastructure for building and verifying
-hybrid systems does not currently exist. Humans have been used for this layer
-because their general intelligence has been relied upon as a safe way to manage
-the hybrid nature of this system. But these operators use prescriptive operating
-manuals to perform their control with strict procedures on what control to
-implement at a given time. These procedures are the key to the operational
-control scope.
+makes it difficult to prove what the behavior of the combined hybrid system will
+do across the entire state-space, so human operators have been used as a
+stop-gap for safety. Humans have been used for this layer because their general
+intelligence has been relied upon as a safe way to manage the hybrid nature of
+this system---if a failure occured, it has been assumed a human operator can
+figure out a solution to maintain plant performance and safety without
+exhaustive knowledge of plant behavior. However, human factors research has
+sought to minimize the need for general human reasoning by creating extremely
+prescriptive operating manuals with strict procedures dictating what control to
+implement at a given time. These operating manuals have minimized the role of
+human operators today, are the key to the automating the operational control
+scope.
 
 The method of constructing a HAHACS in this proposal leverages two key
 observations about current practice. First, the operational scope control is
 effectively discrete control. Second, the rules for implementing this control
-are described prior to their implementation in operating procedures. Before
-constructing a HAHACS, we must completely describe its intended behavior. The
-behavior of any control system originates in requirements: statements about what
-the system must do, must not do, and under what conditions. For nuclear systems,
-these requirements derive from multiple sources including regulatory mandates,
-design basis analyses, and operating procedures. The challenge is formalizing
-these requirements with sufficient precision that they can serve as the
-foundation for autonomous control system synthesis and verification. We can
-build these requirements using temporal logic.
+are described in operating procedures prior to their implementation. Instead of
+implementing these procudures with a human controller, we rigorize the
+instructions as a set of formal requirements. The behavior of any control system
+originates in requirements: statements about what the system must do, must not
+do, and under what conditions. For nuclear systems, these requirements derive
+from multiple sources including regulatory mandates, design basis analyses, and
+aforementioned operating procedures. The challenge is formalizing
+these requirements with sufficient precision that they can serve as
+the foundation for autonomous
+control system synthesis and verification. We can build these requirements using
+temporal logic.
 
-Temporal logic is a powerful set of semantics for building systems with complex
-but deterministic behavior. Temporal logic extends classical propositional logic
-with operators that express properties over time. Using temporal logic, we can
-make statements relating discrete control modes to one another and define all
-the requirements of a HAHACS. The guard conditions $\mathcal{G}$ are defined by
-determining boundary conditions between discrete states and specifying their
-behavior, while continuous mode invariants can also be expressed as temporal
-logic statements. These specifications form the basis of any proofs about a
-HAHACS and constitute the fundamental truth statements about what the behavior
-of the system is designed to be.
+Temporal logic is a powerful set of semantics for building systems with
+complex but deterministic behavior. Temporal logic extends classical
+propositional logic with operators that express properties over time. Using
+temporal logic, we can make statements relating discrete control modes to one
+another and define all the requirements of a HAHACS. The guard conditions
+$\mathcal{G}$ are defined by determining boundary conditions between discrete
+states and specifying their behavior, while continuous mode invariants can
+also be expressed as temporal logic statements. These specifications form the
+basis of any proofs about a HAHACS and constitute the fundamental truth
+statements about what the behavior of the system is designed to be.
 
 Discrete mode transitions include predicates that are Boolean functions over the
 continuous state space: $p_i: \mathcal{X} \rightarrow \{\text{true},
 \text{false}\}$. These predicates formalize conditions like ``coolant
-temperature exceeds 315°C'' or ``pressurizer level is between 30\% and 60\%.''
-Critically, we do not impose this discrete abstraction artificially. Operating
-procedures for nuclear systems already define go/no-go conditions as discrete
-predicates. These thresholds come from design basis safety analysis and have
-been validated over decades of operational experience. Our methodology assumes
-this domain knowledge exists and provides a framework to formalize it. This is
-why the approach is feasible for nuclear applications specifically: the hard
-work of defining safe operating boundaries has already been done by generations
-of nuclear engineers. 
-
-Linear temporal logic (LTL) is particularly well-suited for
-specifying reactive systems. LTL formulas are built from atomic propositions
-(our discrete predicates) using Boolean connectives and temporal operators.
-The key temporal operators are:
-\begin{itemize}
-  \item $\mathbf{X}\phi$ (next): $\phi$ holds in the next state
-  \item $\mathbf{G}\phi$ (globally): $\phi$ holds in all future states
-  \item $\mathbf{F}\phi$ (finally): $\phi$ holds in some future state
-  \item $\phi \mathbf{U} \psi$ (until): $\phi$ holds until $\psi$ becomes true
-\end{itemize}
-These operators allow us to express safety properties (``the reactor never
-enters an unsafe configuration''), liveness properties (``the system
-eventually reaches operating temperature''), and response properties (``if
-coolant pressure drops, the system initiates shutdown within bounded time'').
+temperature exceeds 315\textdegree{}C'' or ``pressurizer level is between 30\%
+and 60\%.'' Critically, we do not impose this discrete abstraction artificially.
+Operating procedures for nuclear systems already define go/no-go conditions as
+discrete predicates, but do so in natural language. These thresholds come from
+design basis safety analysis and have been validated over decades of operational
+experience. Our methodology assumes this domain knowledge exists and provides a
+framework to formalize it. This is why the approach is feasible for nuclear
+applications specifically: the work of defining safe operating boundaries has
+already been done by generations of nuclear engineers. The work of translating
+these requirements from interpretable natural language to a formal
+requirement is what remains to be done.
 
+Linear temporal logic (LTL) is particularly well-suited for specifying reactive
+systems. LTL formulas are built from atomic propositions (our discrete
+predicates) using Boolean connectives and temporal operators. These operators
+allow us to express safety properties (``the reactor never enters an unsafe
+configuration''), liveness properties (``the system eventually reaches operating
+temperature''), and response properties (``if coolant pressure drops, the system
+initiates shutdown within bounded time''). We note that FRET's realizability
+checking currently supports safety and bounded response properties but not
+general liveness properties~\cite{katis_realizability_2022}. Liveness
+requirements such as ``eventually reaches operating temperature'' are instead
+verified through the continuous mode analysis described in Section~3.2, where
+reachability analysis can confirm that target states are attained within bounded
+time.
 
 To build these temporal logic statements, an intermediary tool called FRET is
 planned to be used. FRET stands for Formal Requirements Elicitation Tool, and
 was developed by NASA to build high-assurance timed systems. FRET is an
 intermediate language between temporal logic and natural language that allows
 for rigid definitions of temporal behavior while using a syntax accessible to
-engineers without formal methods expertise. This benefit is crucial for the
-feasibility of this methodology in industry. By reducing the expert knowledge
-required to use these tools, their adoption with the current workforce becomes
-easier.
+engineers without formal methods expertise\cite{katis_realizability_2022}. This
+benefit is crucial for the feasibility of this methodology in industry. By
+reducing the expert knowledge required to use these tools, their adoption with
+the current workforce becomes easier.
 
 A key feature of FRET is the ability to start with logically imprecise
-statements and consecutively refine them into well-posed specifications. We can
-use this to our advantage by directly importing operating procedures and design
-requirements into FRET in natural language, then iteratively refining them into
-specifications for a HAHACS. This has two distinct benefits. First, it allows us
-to draw a direct link from design documentation to digital system
-implementation. Second, it clearly demonstrates where natural language documents
-are insufficient. These procedures may still be used by human operators, so any
-room for interpretation is a weakness that must be addressed.
+statements and consecutively refine them into well-posed
+specifications\cite{katis_realizability_2022, pressburger_using_2023}. We
+can use this to our advantage by directly importing operating procedures and
+design requirements into FRET in natural language, then iteratively refining
+them into specifications for a HAHACS. This has two distinct benefits.
+First, it allows us to draw a direct link from design documentation to
+digital system implementation. Second, it clearly demonstrates where natural
+language documents are insufficient. These procedures may still be used by
+human operators, so any room for interpretation is a weakness that must be
+addressed.
 
-\splitinline{Some examples of where FRET has been used and why it will be successful
-here}
+\dasinline{Maybe add more details about FRET case studies here. This would be
+Pressburger and Katis.}
 
 Once system requirements are defined as temporal logic specifications, we use
 them to build the discrete control system. To do this, reactive synthesis tools
 are employed. Reactive synthesis is a field in computer science that deals with
 the automated creation of reactive programs from temporal logic specifications.
 A reactive program is one that, for a given state, takes an input and produces
-an output. Our systems fit exactly this mold: the current discrete state and
-status of guard conditions are the input, while the output is the next discrete
-state. 
+an output~\cite{jacobs_reactive_2024}. Our systems fit exactly this mold: the
+current discrete state and status of guard conditions are the input, while the
+output is the next discrete state.
 
 Reactive synthesis solves the following problem: given an LTL formula $\varphi$
 that specifies desired system behavior, automatically construct a finite-state
@@ -314,28 +314,35 @@ exists, the specification is called \emph{realizable}. The synthesis algorithm
 either produces a correct-by-construction controller or reports that no such
 controller can exist. This realizability check is itself valuable: an
 unrealizable specification indicates conflicting or impossible requirements in
-the original procedures. 
+the original procedures. The current implementation and one of the main uses of
+FRET today is for exactly this purpose---multiple case studies have used FRET
+for the refinement of unrealizable specifications into realizable systems
+\cite{katis_realizability_2022, pressburger_using_2023}. 
 
 The main advantage of reactive synthesis is that at no point in the production
 of the discrete automaton is human engineering of the implementation required.
-The resultant automaton is correct by construction. This method of construction
-eliminates the possibility of human error at the implementation stage entirely.
-Instead, the effort on the human designer is directed at the specification of
-system behavior itself. This has two critical implications. First, it makes the
-creation of the discrete controller tractable. The reasons the controller
-changes between modes can be traced back to the specification and thus to any
-requirements, which provides a trace for liability and justification of system
-behavior. Second, discrete control decisions made by humans are reliant on the
-human operator operating correctly. Humans are intrinsically probabilistic
-creatures who cannot eliminate human error. By defining the behavior of this
-system using temporal logics and synthesizing the controller using deterministic
-algorithms, we are assured that strategic decisions will always be made
-according to operating procedures.
+The resultant automaton is correct to the specification by construction. This
+method of construction eliminates the possibility of human error at the
+implementation stage entirely. The effort shifts entirely to specifying correct
+behavior rather than implementing it. This has two critical implications. First,
+every mode transition can be traced back through the specification to its
+originating requirement, providing a clear liability and justification chain.
+Second, by defining system behavior in temporal logic and synthesizing the
+controller using deterministic algorithms, discrete control decisions become
+provably consistent with operating procedures. 
 
-\splitinline{Talk about how one would go from a discrete automaton to actual
-code}
-
-\splitinline{Examples of reactive synthesis in the wild}
+The output of reactive synthesis is a finite-state machine that can be directly
+translated to executable code. Tools such as Strix accept full LTL
+specifications and produce Mealy machines via parity game
+solving~\cite{luttenberger_practical_2020, meyer_strix_2018}. For specifications
+within the GR(1) fragment---which captures the reactive input-output structure
+typical of supervisory control---synthesis is efficient and scales to
+specifications with thousands of states. Nuclear operating procedures are
+well-suited to this fragment: environment inputs correspond to plant state
+measurements and guard conditions, while outputs are mode transition commands.
+The synthesized automaton provides a correct-by-construction implementation that
+can be compiled to run on industrial control hardware without manual translation
+of the control logic.
 
 \subsection{Continuous Control Modes}
 
@@ -344,14 +351,15 @@ autonomous controller. These control systems are hybrid, with both discrete and
 continuous components. This section describes the continuous control modes that
 execute within each discrete state, and how we verify that they satisfy the
 requirements imposed by the discrete layer. It is important to clarify the scope
-of this methodology with respect to continuous controller design. This work
-verifies continuous controllers; it does not synthesize them. The distinction
+of this methodology with respect to continuous controller design. This work will
+verify continuous controllers; it does not synthesize them. The distinction
 parallels model checking in software verification: model checking does not tell
 engineers how to write correct software, but it verifies whether a given
 implementation satisfies its specification. Similarly, we assume that continuous
-controllers can be designed using standard control theory techniques. Our
-contribution is a verification framework that confirms candidate controllers
-compose correctly with the discrete layer to produce a safe hybrid system.
+controllers can be designed using standard control theory techniques, and to
+that end, are not prohibitive to create. Our contribution is a verification
+framework that confirms candidate controllers compose correctly with the
+discrete layer to produce a safe hybrid system.
 
 The operational control scope defines go/no-go decisions that determine what
 kind of continuous control to implement. The entry or exit conditions of a
@@ -359,12 +367,12 @@ discrete state are themselves the guard conditions $\mathcal{G}$ that define the
 boundaries for each continuous controller's allowed state-space region. These
 continuous controllers all share a common state space, but each individual
 continuous control mode operates within its own partition defined by the
-discrete state $q_i$ and the associated guards. This partitioning of the
-continuous state space among several discrete vector fields has traditionally
-been a difficult problem for validation and verification. The discontinuity of
-the vector fields at discrete state interfaces makes reachability analysis
-computationally expensive, and analytic solutions often become intractable
-\cite{kapuria2025, lang2021}.
+discrete state $q_i$ and the associated guard conditions. This partitioning of
+the continuous state space among several distinct vector fields has
+traditionally been a difficult problem for validation and verification. The
+discontinuity of the vector fields at discrete state interfaces makes
+reachability analysis computationally expensive, and analytic solutions often
+become intractable \cite{kapuria_using_2025, lang_formal_2021}.
 
 We circumvent these issues by designing our hybrid system from the bottom up
 with verification in mind. Each continuous control mode has an input set and
@@ -372,201 +380,235 @@ output set clearly defined by our discrete transitions \textit{a priori}.
 Consider that we define the continuous state space as $\mathcal{X}$. Each
 discrete mode $q_i$ then provides three key pieces of information for continuous
 controller design:
+%
 \begin{enumerate}
-  \item \textbf{Entry conditions:} $\mathcal{X}_{entry,i} \subseteq \mathcal{X}$,
-    the set of possible initial states when entering this mode
-  \item \textbf{Exit conditions:} $\mathcal{X}_{exit,i} \subseteq \mathcal{X}$,
-    the target states that trigger transition to the next mode, or is the region
-    in the state space a stabilizing mode remains within.
-  \item \textbf{Safety invariants:} $\mathcal{X}_{safe,i} \subseteq \mathcal{X}$,
-    the envelope of safe states during operation in this mode. These are derived
-    from invariants \(Inv\).
+  \item \textbf{Entry conditions:} $\mathcal{X}_{entry,i} \subseteq
+    \mathcal{X}$, the set of possible initial states when entering this mode
+  \item \textbf{Exit conditions:} $\mathcal{X}_{exit,i} \subseteq
+    \mathcal{X}$, the target states that trigger transition to the next mode,
+    or is the region in the state space a stabilizing mode remains within.
+  \item \textbf{Safety invariants:} $\mathcal{X}_{safe,i} \subseteq
+    \mathcal{X}$, the envelope of safe states during operation in this mode.
+    These are derived from invariants \(Inv\).
 \end{enumerate}
+%
 These sets come directly from the discrete controller synthesis and define
-precise objectives for continuous control. The continuous controller for mode
-$q_i$ must drive the system from any state in $\mathcal{X}_{entry,i}$ to some
-state in $\mathcal{X}_{exit,i}$ while remaining within $\mathcal{X}_{safe,i}$.
+precise objectives for continuous control.\dasnote{This SOUNDS like
+assume-guarantee stuff. Maybe make that connection formal and cite it?} The
+continuous controller for mode $q_i$ must drive the system from any state in
+$\mathcal{X}_{entry,i}$ to some state in $\mathcal{X}_{exit,i}$ while remaining
+within $\mathcal{X}_{safe,i}$. We classify continuous controllers into three
+types based on their objectives: transitory, stabilizing, and expulsory. Each
+type has distinct verification requirements that determine which formal methods
+tools are appropriate.
 
-We classify continuous controllers into three types based on their objectives:
-transitory, stabilizing, and expulsory. Each type has distinct verification
-requirements that determine which formal methods tools are appropriate.
+\dasinline{(1) Add figure showing the relationship between entry/exit/safety
+sets. (2) Mention assume-guarantee compositional stuff and how that fits in
+here.}
 
 \subsubsection{Transitory Modes}
 
-Transitory modes are continuous controllers designed to move
-the plant from one discrete operating condition to another. Their purpose is to
-execute transitions: starting from entry conditions, reach exit conditions,
-and maintain safety invariants throughout. Examples include power ramp-up sequences,
-cooldown procedures, and load-following maneuvers.
+Transitory modes are continuous controllers designed to move the plant from one
+discrete operating condition to another. Their purpose is to execute
+transitions: starting from entry conditions, reach exit conditions, and maintain
+safety invariants throughout. Examples include but are not limited to power
+ramp-up sequences, cooldown procedures, and load-following maneuvers.
 
-The control objective for a transitory mode can be stated
-formally. Given entry conditions $\mathcal{X}_{entry}$, exit conditions
-$\mathcal{X}_{exit}$, safety invariant $\mathcal{X}_{safe}$, and closed-loop
-dynamics $\dot{x} = f(x, u(x))$, the controller must satisfy:
+The control objective for a transitory mode can be stated formally. Given
+entry conditions $\mathcal{X}_{entry}$, exit conditions
+$\mathcal{X}_{exit}$, safety invariant $\mathcal{X}_{safe}$, and
+closed-loop dynamics $\dot{x} = f(x)$, the controller must satisfy:
+%
 \[
-\forall x_0 \in \mathcal{X}_{entry}: \exists T > 0: x(T) \in \mathcal{X}_{exit}
-\land \forall t \in [0,T]: x(t) \in \mathcal{X}_{safe}
+\forall x_0 \in \mathcal{X}_{entry}: \exists T > 0: x(T) \in
+\mathcal{X}_{exit} \land \forall t \in [0,T]: x(t) \in \mathcal{X}_{safe}
 \]
+%
 That is, from any valid entry state, the trajectory must eventually reach the
 exit condition without ever leaving the safe region.
 
-Verification of transitory modes uses reachability analysis.
-Reachability analysis computes the set of all states reachable from a given
-initial set under the system dynamics. For a transitory mode to be valid, the
-reachable set from $\mathcal{X}_{entry}$ must satisfy two conditions:
+Verification of transitory modes will use reachability analysis. Reachability
+analysis computes the set of all states reachable from a given initial set under
+the system dynamics~\cite{guernic_reachability_2009,
+mitchell_time-dependent_2005, bansal_hamilton-jacobi_2017}. For a transitory
+mode to be valid, the reachable set from $\mathcal{X}_{entry}$ must satisfy two
+conditions:
+%
 \begin{enumerate}
-  \item The reachable set eventually intersects $\mathcal{X}_{exit}$ (the mode
-    achieves its objective)
-  \item The reachable set never leaves $\mathcal{X}_{safe}$ (safety is maintained
-    throughout the transition)
+  \item The reachable set eventually intersects $\mathcal{X}_{exit}$ (the
+    mode achieves its objective)
+  \item The reachable set never leaves $\mathcal{X}_{safe}$ (safety is
+    maintained throughout the transition)
 \end{enumerate}
+%
 Formally, if $\text{Reach}(\mathcal{X}_{entry}, f, [0,T])$ denotes the states
 reachable within time horizon $T$:
+%
 \[
-\text{Reach}(\mathcal{X}_{entry}, f_i, [0,T]) \subseteq \mathcal{X}_{safe} \land
-\text{Reach}(\mathcal{X}_{entry}, f_i, [0,T]) \cap \mathcal{X}_{exit} \neq \emptyset
+\text{Reach}(\mathcal{X}_{entry}, f_i, [0,T]) \subseteq \mathcal{X}_{safe}
+\land \text{Reach}(\mathcal{X}_{entry}, f_i, [0,T]) \cap
+\mathcal{X}_{exit} \neq \emptyset
 \]
+%
+Because the discrete controller defines clear boundaries in
+continuous state space, the verification problem for each transitory mode is
+well-posed. We know the possible initial conditions, we know the target
+conditions, and we know the safety envelope. The verification task is to
+confirm that the candidate continuous controller achieves the objective from
+all possible starting points.
 
-Because the discrete controller defines clear boundaries in continuous state
-space, the verification problem for each transitory mode is well-posed. We know
-the possible initial conditions, we know the target conditions, and we know the
-safety envelope. The verification task is to confirm that the candidate
-continuous controller achieves the objective from all possible starting points.
-
-Several tools exist for computing reachable sets of hybrid
-systems, including CORA, Flow*, SpaceEx, and JuliaReach. The choice of tool
-depends on the structure of the continuous dynamics. Linear systems admit
-efficient polyhedral or ellipsoidal reachability computations. Nonlinear
-systems require more conservative over-approximations using techniques such as
-Taylor models or polynomial zonotopes. For this work, we will select tools
-appropriate to the fidelity of the reactor models available.
+Several tools exist for computing reachable sets of hybrid systems, including
+CORA~\cite{althoff_introduction_nodate}, Flow*~\cite{chen_flow_2013,
+chen_taylor_2012}, SpaceEx~\cite{frehse_spaceex_2011}, and
+JuliaReach~\cite{bogomolov_reachability_2020}. The choice of
+tool depends on the structure of the continuous dynamics. Linear systems admit
+efficient polyhedral or ellipsoidal reachability computations. Nonlinear systems
+require more conservative over-approximations using techniques such as Taylor
+models or polynomial zonotopes. For this work, we will select tools appropriate
+to the fidelity of the reactor models available.
 
 \subsubsection{Stabilizing Modes}
 
-Stabilizing modes are continuous controllers with an objective of maintaining a
-particular discrete state indefinitely. Rather than driving the system toward an
-exit condition, they keep the system within a safe operating region. Examples
-include steady-state power operation, hot standby, and load-following at
-constant power level. Reachability analysis for stabilizing modes may not be a
-suitable approach to validation. Instead, we plan to use barrier certificates.
-Barrier certificates analyze the dynamics of the system to determine whether
-flux across a given boundary exists. They evaluate whether any trajectory leaves
-a given boundary. This definition is exactly what defines the validity of a
-stabilizing continuous control mode.
+Stabilizing modes are continuous controllers with an objective of maintaining
+a particular discrete state indefinitely. Rather than driving the system
+toward an exit state, they keep the system within a safe
+operating region. Examples include steady-state power operation, hot standby,
+and load-following at constant power level. Reachability analysis for
+stabilizing modes may not be a suitable approach to validation. Instead, we
+plan to use barrier certificates. Barrier certificates analyze the dynamics
+of the system to determine whether flux across a given boundary
+exists~\cite{prajna_safety_2004}. In other words, they
+evaluate whether any trajectory leaves a given boundary. This definition is
+exactly what defines the validity of a stabilizing continuous control mode.
 
-A barrier certificate (or control barrier function) is a
-scalar function $B: \mathcal{X} \rightarrow \mathbb{R}$ that certifies forward
-invariance of a safe set. The idea is analogous to Lyapunov functions for
-stability: rather than computing trajectories explicitly, we find a certificate
-function whose properties guarantee the desired behavior. For a safe set
-$\mathcal{C} = \{x : B(x) \geq 0\}$ and dynamics $\dot{x} = f(x,u)$, the
-barrier certificate condition requires:
+A barrier certificate (or control barrier function) is a scalar function $B:
+\mathcal{X} \rightarrow \mathbb{R}$ that certifies forward invariance of a safe
+set. The idea is analogous to Lyapunov functions for
+stability~\cite{branicky_multiple_1998}: rather than computing trajectories
+explicitly, we find a certificate function whose properties guarantee the
+desired behavior. For a safe set $\mathcal{C} = \{x : B(x) \geq 0\}$ and
+dynamics $\dot{x} = f(x,u)$, the\dasinline{Should clarify that the safe set C is
+not the entire continuous region. It's just the boundary of the region.} barrier
+certificate condition requires:
+%
 \[
-\forall x \in \partial\mathcal{C}: \dot{B}(x) = \nabla B(x) \cdot f(x,u(x)) \geq 0
+\forall x \in \partial\mathcal{C}: \dot{B}(x) = \nabla B(x) \cdot f(x,u(x))
+\geq 0
 \]
-This condition states that on the boundary of the safe set (where $B(x) = 0$),
-the time derivative of $B$ is non-negative. Geometrically, this means the
-vector field points inward or tangent to the boundary, never outward. If this
-condition holds, no trajectory starting inside $\mathcal{C}$ can ever leave.
+%
+This condition states that on the boundary of the safe set (where $B(x) =
+0$), the time derivative of $B$ is non-negative. Geometrically, this means
+the vector field points inward or tangent to the boundary, never outward. If
+this condition holds, no trajectory starting inside $\mathcal{C}$ can ever
+leave.
 
 Because the design of the discrete controller defines careful boundaries in
-continuous state space, the barrier is known prior to designing the continuous
-controller. This eliminates the search for an appropriate barrier and minimizes
-complication in validating stabilizing continuous control modes. The discrete
-specifications tell us what region must be invariant; the barrier certificate
-confirms that the candidate controller achieves this invariance.
+continuous state space, the barrier \(\mathcal{C}\) is known prior to designing
+the continuous controller. This eliminates the search for an appropriate barrier
+and minimizes complication in validating stabilizing continuous control modes.
+The discrete specifications tell us what region must be invariant; the barrier
+certificate confirms that the candidate controller achieves this invariance.
 
-Finding barrier certificates can be formulated as a
-sum-of-squares (SOS) optimization problem for polynomial systems, or solved
-using satisfiability modulo theories (SMT) solvers for broader classes of
-dynamics. The key advantage is that the verification is independent of how
-the controller was designed. Standard control techniques can be used to
-build continuous controllers, and barrier certificates provide a separate
-check that the result satisfies the required invariants. This also allows for
-the checking of control modes with different models than they are designed for.
-For example, a lower fidelity model can be used for controller design, but a
-higher fidelity model can be used for the actual validation of that stabilizing
-controller.
+The key advantage is that the verification is independent of how the controller
+was designed. Standard control techniques can be used to build continuous
+controllers, and barrier certificates provide a separate check that the result
+satisfies the required invariants. This also allows for the checking of control
+modes with different models than they are designed for. For example, a lower
+fidelity model can be used for controller design, but a higher fidelity model
+can be used for the actual validation of that stabilizing
+controller.\splitnote{SOS methods proven effective: Papachristodoulou 2021
+  (SOSTOOLS v4, pp.1-2) solves barrier certificate optimization via SOS
+  constraints---tool integrates with MATLAB. Borrmann 2015 (pp.4-8) demonstrates
+  control barrier certificates for multi-agent systems, showing how discrete
+  boundaries (mode guards) can inform barrier design. Your claim that discrete
+  specs eliminate barrier search is novel and well-supported by these
+foundations.}\splitnote{Hauswirth 2024 (pp.1-3) shows optimization-based robust
+  feedback controllers can serve as alternative verification method---suggests
+  barrier certificates + reachability provide complementary guarantees for your
+stabilizing modes.}
 
 \subsubsection{Expulsory Modes}
 
-Expulsory modes are continuous controllers responsible for
-ensuring safety when failures occur. They are designed for robustness rather
-than optimality. The control objective is to drive the plant to a safe shutdown
-state from potentially anywhere in the state space, under degraded or uncertain
-dynamics. Examples include emergency core cooling, reactor SCRAM sequences, and
-controlled depressurization procedures.
+Expulsory modes are continuous controllers responsible for ensuring safety
+when failures occur. They are designed for robustness rather than optimality.
+The control objective is to drive the plant to a safe shutdown state from
+potentially anywhere in the state space, under degraded or uncertain
+dynamics. Examples include emergency core cooling, reactor SCRAM sequences,
+and controlled depressurization procedures.
 
 We can detect that physical failures exist because our physical controllers have
 been previously proven correct by reachability and barrier certificates. We know
 our controller cannot be incorrect for the nominal plant model, so if an
-invariant is violated, we know the plant dynamics have changed. The HAHACS can
-identify that a fault occurred because a discrete boundary condition was
-violated by the continuous physical controller. This is a direct consequence of
-having verified the nominal continuous control modes: unexpected behavior
-implies off-nominal conditions.
-
-The mathematical formulation for expulsory mode verification
-differs from transitory modes in two key ways. First, the entry conditions may
-be the entire state space (or a large, conservatively bounded region) rather
-than a well-defined entry set. The failure may occur at any point during
-operation. Second, the dynamics include parametric uncertainty representing
-failure modes:
+invariant is violated, we know the plant dynamics have changed. The mathematical
+formulation for expulsory mode verification differs from transitory modes in two
+key ways. First, the entry conditions may be the entire state space (or a large,
+conservatively bounded region) rather than a well-defined entry set. The failure
+may occur at any point during operation. Second, the dynamics include parametric
+uncertainty representing failure modes:
+%
 \[
 \dot{x} = f(x, u, \theta), \quad \theta \in \Theta_{failure}
 \]
+%
 where $\Theta_{failure}$ captures the range of possible degraded plant
 behaviors identified through failure mode and effects analysis (FMEA) or
 traditional safety analysis. 
 
 We verify expulsory modes using reachability analysis with parametric
-uncertainty. The verification condition requires that for all parameter values
-within the uncertainty set, trajectories from the expanded entry region reach
-the safe shutdown state:
+uncertainty. While tools such as SpaceEx handle nondeterministic
+inputs~\cite{frehse_spaceex_2011}, parametric plant uncertainty requires
+conservative over-approximation of reachable sets across the full parameter
+range. The verification condition requires that for all parameter values within
+the uncertainty set, trajectories from the expanded entry region reach the safe
+shutdown state:
+%
 \[
 \forall \theta \in \Theta_{failure}:
-\text{Reach}(\mathcal{X}_{current}, f_\theta, [0,T]) \subseteq \mathcal{X}_{shutdown}
+\text{Reach}(\mathcal{X}_{current}, f_\theta, [0,T]) \subseteq
+\mathcal{X}_{shutdown}
 \]
+%
 This is more conservative than nominal reachability, accounting for the fact
 that we cannot know exactly which failure mode is active.
 
-Traditional safety analysis techniques inform the construction
-of $\Theta_{failure}$. Probabilistic risk assessment, FMEA, and design basis
+Traditional safety analysis techniques inform the construction of
+$\Theta_{failure}$. Probabilistic risk assessment, FMEA, and design basis
 accident analysis identify credible failure scenarios and their effects on
 plant dynamics. The expulsory mode must handle the worst-case dynamics within
 this envelope. This is where conservative controller design is appropriate as
-safety margins will matter more than performance during emergency shutdown.
+safety margins will matter more than performance during emergency
+shutdown.\splitnote{Parametric uncertainty approach validated: Kapuria 2025
+(pp.82-120, Sections 5) verifies SmAHTR resiliency against UCAs with
+uncertain dynamics (e.g., PHX secondary flow shutdown, resonating turbine
+flow). Uses reachability + Z3 SMT solver (pp.23-24, Section 2.5 on
+$\delta$-SAT) to handle nonlinear uncertainty---demonstrates your expulsory
+mode approach is sound for nuclear failures. Shows safety can be proven even
+when controller deviates from nominal (pp.85-107, UCA 1
+analysis).}
 
 \subsection{Industrial Implementation}
 
-The methodology described above must be validated on realistic
-systems using industrial-grade hardware to demonstrate practical feasibility.
-This research will leverage the University of Pittsburgh Cyber Energy Center's
-partnership with Emerson to implement and test the HAHACS methodology on
-production control equipment. Emerson's Ovation distributed control system is widely deployed
-in power generation facilities, including nuclear plants. The Ovation platform
-provides a realistic target for demonstrating that formally synthesized
-controllers can execute on industrial hardware meeting timing and reliability
-requirements. The discrete automaton produced by reactive synthesis will be
-compiled to run on Ovation controllers, with verification that the implemented
-behavior matches the synthesized specification exactly.
+The methodology described above must be validated on realistic systems using
+industrial-grade hardware to demonstrate practical feasibility. This research
+will leverage the University of Pittsburgh Cyber Energy Center's partnership
+with Emerson to implement and test the HAHACS methodology on production
+control equipment. Emerson's Ovation distributed control system is widely
+deployed in power generation facilities, including nuclear plants. The
+Ovation platform provides a realistic target for demonstrating that formally
+synthesized controllers can execute on industrial hardware meeting timing and
+reliability requirements. The discrete automaton produced by reactive
+synthesis will be compiled to run on Ovation controllers, with verification
+that the implemented behavior matches the synthesized specification exactly.
 
-For the continuous dynamics, we will use a small modular
-reactor simulation. The SmAHTR (Small modular Advanced High Temperature
-Reactor) model provides a relevant testbed for startup and shutdown procedures.
-The ARCADE (Advanced Reactor Control Architecture Development Environment)
-interface will establish communication between the Emerson Ovation hardware and
-the reactor simulation, enabling hardware-in-the-loop testing of the complete
-hybrid controller.
-
-Working with Emerson on such an implementation is an incredible advantage for
-the success and impact of this work. We will directly address the gap of
-verification and validation methods for these systems and industry adoption by
-forming a two-way exchange of knowledge between the laboratory and commercial
-environments. This work stands to be successful with Emerson implementation
-because we will have access to system experts at Emerson to help with the fine
-details of using the Ovation system. At the same time, we will have the benefit
-of transferring technology directly to industry with a direct collaboration in
-this research, while getting an excellent perspective of how our research
-outcomes can align best with customer needs.
+For the continuous dynamics, we will use a small modular reactor simulation. The
+SmAHTR (Small modular Advanced High Temperature Reactor) model provides a
+relevant testbed for startup and shutdown procedures. The ARCADE (Advanced
+Reactor Control Architecture Development Environment) interface will establish
+communication between the Emerson Ovation hardware and the reactor simulation,
+enabling hardware-in-the-loop testing of the complete hybrid controller.
 
+The Emerson collaboration strengthens this work in two ways. Access to
+system experts at Emerson ensures that implementation details of the Ovation
+platform are handled correctly. Direct industry collaboration also provides an
+immediate pathway for technology transfer and alignment with practical
+deployment requirements.

4-metrics-of-success/metrics.tex

@@ -1,33 +1,17 @@
 \section{Metrics for Success}
 
 This research will be measured by advancement through Technology Readiness
-Levels, progressing from fundamental concepts to validated prototype
-demonstration. This work begins at TRL 2--3 and aims to reach TRL 5, where
-system components operate successfully in a relevant laboratory 
-environment. This section explains why TRL advancement provides the most appropriate success
-metric and defines the specific criteria required to achieve TRL 5.
-
-Technology Readiness Levels provide the ideal success metric because they
-explicitly measure the gap between academic proof-of-concept and practical
-deployment---precisely what this work aims to bridge. Academic metrics like
-papers published or theorems proved cannot capture practical feasibility.
-Empirical metrics like simulation accuracy or computational speed cannot
-demonstrate theoretical rigor. TRLs measure both dimensions 
-simultaneously. Advancing from TRL 3 to TRL 5 requires maintaining theoretical rigor while
-progressively demonstrating practical feasibility. Formal verification must
-remain valid as the system moves from individual components to integrated
-hardware testing.
-
-The nuclear industry requires extremely high assurance before deploying new
-control technologies. Demonstrating theoretical correctness alone is
-insufficient for adoption; conversely, showing empirical performance without
-formal guarantees fails to meet regulatory requirements. TRLs capture this dual
-requirement naturally. Each level represents both increased practical maturity
-and sustained theoretical validity. Furthermore, TRL assessment forces explicit
-identification of remaining barriers to deployment. The nuclear industry already
-uses TRLs for technology assessment, making this metric directly relevant to
-potential adopters. Reaching TRL 5 provides a clear answer to industry questions
-about feasibility and maturity that academic publications alone cannot.
+Levels (TRL), progressing from fundamental concepts to validated prototype
+demonstration. TRLs measure the gap between academic proof-of-concept and
+practical deployment, which is precisely what this work aims to bridge. Academic
+metrics alone cannot capture practical feasibility, and empirical metrics alone
+cannot demonstrate theoretical rigor. TRLs measure both simultaneously. This
+work begins at TRL 2--3 and aims to reach TRL 5, where system components operate
+successfully in a relevant laboratory environment. This section explains why TRL
+advancement provides the most appropriate success metric and defines the
+specific criteria required to achieve TRL 5. Reaching TRL 5 provides a clear
+answer to industry questions about feasibility and maturity that academic
+publications alone cannot.
 
 Moving from current state to target requires achieving three intermediate
 levels, each representing a distinct validation milestone:
@@ -40,8 +24,8 @@ temporal logic specifications that pass realizability analysis. A discrete
 automaton must be synthesized with interpretable structure. At least one
 continuous controller must be designed with reachability analysis proving
 transition requirements are satisfied. Independent review must confirm that
-specifications match intended procedural behavior. This proves the fundamental
-approach on a simplified startup sequence.
+specifications match intended procedural behavior. This proves the
+fundamental approach on a simplified startup sequence.
 
 \paragraph{TRL 4 \textit{Laboratory Testing of Integrated Components}}
 
@@ -52,8 +36,8 @@ must exist for all discrete modes. Verification must be complete for all mode
 transitions using reachability analysis, barrier certificates, and
 assume-guarantee contracts. The integrated controller must execute complete
 startup sequences in software simulation with zero safety violations across
-multiple consecutive runs. This proves that formal correctness guarantees can be
-maintained throughout system integration.
+multiple consecutive runs. This proves that formal correctness guarantees can
+be maintained throughout system integration.
 
 \paragraph{TRL 5 \textit{Laboratory Testing in Relevant Environment}}
 
@@ -68,11 +52,10 @@ across the full operational envelope. The controller must handle off-nominal
 scenarios to validate that expulsory modes function correctly. For example,
 simulated sensor failures must trigger appropriate fault detection and mode
 transitions, and loss-of-cooling scenarios must activate SCRAM procedures as
-specified. Graded responses to minor disturbances are outside this work's scope.
-If this work is successful, graded responses are an extension that requires
-additional labor, but not new capability as the mechanics of a graded response
-are an addition of special discrete modes and continuous controllers to match.
-Formal verification results must remain valid, with discrete behavior matching
+specified. Graded responses to minor disturbances are outside this work's scope,
+as they require runtime optimization under uncertainty that extends beyond the
+correct-by-construction verification framework presented here. Formal
+verification results must remain valid, with discrete behavior matching
 specifications and continuous trajectories remaining within verified bounds.
 This proves that the methodology produces verified controllers implementable on
 industrial hardware.
@@ -81,12 +64,12 @@ Progress will be assessed quarterly through collection of specific data
 comparing actual results against TRL advancement criteria. Specification
 development status indicates progress toward TRL 3. Synthesis results and
 verification coverage indicate progress toward TRL 4. Simulation performance
-metrics and hardware integration milestones indicate progress toward TRL 5. The
-research plan will be revised only when new data invalidates fundamental
+metrics and hardware integration milestones indicate progress toward TRL 5.
+The research plan will be revised only when new data invalidates fundamental
 assumptions. This research succeeds if it achieves TRL 5 by demonstrating a
 complete autonomous hybrid controller with formal correctness guarantees
-operating on industrial control hardware through hardware-in-the-loop testing in
-a relevant laboratory environment. This establishes both theoretical validity
-and practical feasibility, proving that the methodology produces verified
-controllers and that implementation is achievable with current 
-technology.
+operating on industrial control hardware through hardware-in-the-loop
+testing in a relevant laboratory environment. This establishes both
+theoretical validity and practical feasibility, proving that the methodology
+produces verified controllers and that implementation is achievable with
+current technology.

5-risks-and-contingencies/risks.tex

@@ -1,9 +1,10 @@
 \section{Risks and Contingencies}
 
-This research relies on several critical assumptions that, if invalidated, would
-require scope adjustment or methodological revision. The primary risks to
-successful completion fall into four categories: computational tractability of
-synthesis and verification, complexity of the discrete-continuous interface,
+This research relies on several critical assumptions that, if invalidated,
+would require scope adjustment or methodological
+revision. The primary risks to successful
+completion fall into four categories: computational tractability of synthesis
+and verification, complexity of the discrete-continuous interface,
 completeness of procedure formalization, and hardware-in-the-loop integration
 challenges. Each risk has associated indicators for early detection and
 contingency plans that preserve research value even if core assumptions prove
@@ -15,21 +16,22 @@ deployment.
 
 The first major assumption is that formalized startup procedures will yield
 automata small enough for efficient synthesis and verification. Reactive
-synthesis scales exponentially with specification complexity, creating risk that
-temporal logic specifications derived from complete startup procedures may
-produce automata with thousands of states. Such large automata would require
-synthesis times exceeding days or weeks, preventing demonstration of the
-complete methodology within project timelines. Reachability analysis for
+synthesis scales exponentially with specification complexity, creating risk
+that temporal logic specifications derived from complete startup procedures
+may produce automata with thousands of states. Such large automata would
+require synthesis times exceeding days or weeks, preventing demonstration of
+the complete methodology within project timelines. Reachability analysis for
 continuous modes with high-dimensional state spaces may similarly prove
 computationally intractable. Either barrier would constitute a fundamental
 obstacle to achieving the research objectives.
 
 Several indicators would provide early warning of computational tractability
 problems. Synthesis times exceeding 24 hours for simplified procedure subsets
-would suggest complete procedures are intractable. Generated automata containing
-more than 1,000 discrete states would indicate the discrete state space is too
-large for efficient verification. Specifications flagged as unrealizable by FRET
-or Strix would reveal fundamental conflicts in the formalized procedures.
+would suggest complete procedures are intractable. Generated automata
+containing more than 1,000 discrete states would indicate the discrete state
+space is too large for efficient verification. Specifications flagged as
+unrealizable by realizability checking
+tools would reveal fundamental conflicts in the formalized procedures.
 Reachability analysis failing to converge within reasonable time bounds would
 show that continuous mode verification cannot be completed with available
 computational resources.
@@ -37,95 +39,127 @@ computational resources.
 The contingency plan for computational intractability is to reduce scope to a
 minimal viable startup sequence. This reduced sequence would cover only cold
 shutdown to criticality to low-power hold, omitting power ascension and other
-operational phases. The subset would still demonstrate the complete methodology
-while reducing computational burden. The research contribution would remain
-valid even with reduced scope, proving that formal hybrid control synthesis is
-achievable for safety-critical nuclear applications. The limitation to
-simplified operational sequences would be explicitly documented as a constraint
-rather than a failure.
+operational phases. The subset would still demonstrate the complete
+methodology while reducing computational burden. The research contribution
+would remain valid even with reduced scope, proving that formal hybrid
+control synthesis is achievable for safety-critical nuclear applications. The
+limitation to simplified operational sequences would be explicitly documented
+as a constraint rather than a failure.
 
 \subsection{Discrete-Continuous Interface Formalization}
 
 The second critical assumption concerns the mapping between boolean guard
 conditions in temporal logic and continuous state boundaries required for mode
 transitions. This interface represents the fundamental challenge of hybrid
-systems: relating discrete switching logic to continuous dynamics. Guard conditions
-requiring complex predicates may resist boolean abstraction, making
-synthesis intractable. Continuous safety regions that cannot be expressed as
-conjunctions of verifiable constraints would similarly create insurmountable
-verification challenges. The risk extends beyond static interface definition to
-dynamic behavior across transitions: barrier certificates may fail to exist for
-proposed transitions, or continuous modes may be unable to guarantee convergence
-to discrete transition boundaries.
+systems: relating discrete switching logic to continuous dynamics. Temporal
+logic operates on boolean predicates, while continuous control requires
+reasoning about differential equations and reachable sets. Some guard conditions
+may require complex nonlinear predicates that cannot be cleanly expressed as
+boolean combinations of simple threshold checks, making synthesis intractable.
+Continuous safety regions that cannot be expressed as conjunctions of verifiable
+constraints would similarly create insurmountable verification challenges. The
+risk extends beyond static interface definition to dynamic behavior across
+transitions: barrier certificates may fail to exist for proposed transitions, or
+continuous modes may be unable to guarantee convergence to discrete transition
+boundaries.
 
 Early indicators of interface formalization problems would appear during both
-synthesis and verification phases. Guard conditions requiring complex nonlinear
-predicates that resist boolean abstraction would suggest fundamental misalignment
-between discrete specifications and continuous realities. Continuous safety
-regions that cannot be expressed as conjunctions of half-spaces or polynomial
-inequalities would indicate the interface between discrete guards and continuous
-invariants is too complex. Failure to construct barrier certificates proving
-safety across mode transitions would reveal that continuous dynamics cannot be
-formally related to discrete switching logic. Reachability analysis showing that
-continuous modes cannot reach intended transition boundaries from all possible
-initial conditions would demonstrate the synthesized discrete controller is
-incompatible with achievable continuous behavior.
+synthesis and verification phases. Guard conditions requiring complex
+nonlinear predicates that resist boolean abstraction would suggest
+fundamental misalignment between discrete specifications and continuous
+realities. Continuous safety regions that cannot be expressed as conjunctions
+of half-spaces or polynomial inequalities would indicate the interface
+between discrete guards and continuous invariants is too complex. Failure to
+construct barrier certificates proving safety across mode transitions would
+reveal that continuous dynamics cannot be formally related to discrete
+switching logic. Reachability analysis showing that continuous modes cannot
+reach intended transition boundaries from all possible initial conditions
+would demonstrate the synthesized discrete controller is incompatible with
+achievable continuous behavior.
 
-The primary contingency for interface complexity is restricting continuous modes
-to operate within polytopic invariants. Polytopes are state regions defined as
-intersections of linear half-spaces, which map directly to boolean predicates
-through linear inequality checks. This restriction ensures tractable synthesis
-while maintaining theoretical rigor, though at the cost of limiting
-expressiveness compared to arbitrary nonlinear regions. The discrete-continuous
-interface remains well-defined and verifiable with polytopic restrictions,
-providing a clear fallback position that preserves the core methodology.
-Conservative over-approximations offer an alternative approach: a nonlinear safe
-region can be inner-approximated by a polytope, sacrificing operational
-flexibility to maintain formal guarantees. The three-mode classification already
-structures the problem to minimize complex transitions, with critical safety
-properties concentrated in expulsory modes that can receive additional design
-attention.
+The primary contingency for interface complexity is restricting continuous
+modes to operate within polytopic invariants. Polytopes are state regions
+defined as intersections of linear half-spaces, which map directly to boolean
+predicates through linear inequality checks. This restriction ensures
+tractable synthesis while maintaining theoretical rigor, though at the cost
+of limiting expressiveness compared to arbitrary nonlinear regions. The
+discrete-continuous interface remains well-defined and verifiable with
+polytopic restrictions, providing a clear fallback position that preserves
+the core methodology. Conservative over-approximations offer an alternative
+approach: a nonlinear safe region can be inner-approximated by a polytope,
+sacrificing operational flexibility to maintain formal guarantees. The
+three-mode classification already structures the problem to minimize complex
+transitions, with critical safety properties concentrated in expulsory modes
+that can receive additional design attention.
+
+Mitigation strategies focus on designing continuous controllers with discrete
+transitions as primary objectives from the outset. Rather than designing
+continuous control laws independently and verifying transitions post-hoc, the
+approach uses transition requirements as design constraints. Control barrier
+functions provide a systematic method to synthesize controllers that
+guarantee forward invariance of safe sets and convergence to transition
+boundaries. This design-for-verification approach reduces the likelihood that
+interface complexity becomes insurmountable. Focusing verification effort on
+expulsory modes---where safety is most critical---allows more complex
+analysis to be applied selectively rather than uniformly across all modes,
+concentrating computational resources where they matter most for safety
+assurance.
 
 \subsection{Procedure Formalization Completeness}
 
 The third assumption is that existing startup procedures contain sufficient
-detail and clarity for translation into temporal logic specifications. Nuclear
-operating procedures, while extensively detailed, were written for human
-operators who bring contextual understanding and adaptive reasoning to their
-interpretation. Procedures may contain implicit knowledge, ambiguous directives,
-or references to operator judgment that resist formalization in current
-specification languages. Underspecified timing constraints, ambiguous condition
-definitions, or gaps in operational coverage would cause synthesis to fail or
-produce incorrect automata. The risk is not merely that formalization is
-difficult, but that current procedures fundamentally lack the precision required
-for autonomous control, revealing a gap between human-oriented documentation and
-machine-executable specifications.
+detail and clarity for translation into temporal logic specifications.
+Nuclear operating procedures, while extensively detailed, were written for
+human operators who bring contextual understanding and adaptive reasoning to
+their interpretation. Procedures may contain implicit knowledge, ambiguous
+directives, or references to operator judgment that resist formalization in
+current specification languages. Underspecified timing constraints, ambiguous
+condition definitions, or gaps in operational coverage would cause synthesis
+to fail or produce incorrect automata. The risk is not merely that
+formalization is difficult, but that current procedures fundamentally lack
+the precision required for autonomous control, revealing a gap between
+human-oriented documentation and machine-executable specifications.
 
-Several indicators would reveal formalization completeness problems early in the
-project. FRET realizability checks failing due to underspecified behaviors or
-conflicting requirements would indicate procedures do not form a complete
-specification. Multiple valid interpretations of procedural steps with no clear
-resolution would demonstrate procedure language is insufficiently precise for
-automated synthesis. Procedures referencing ``operator judgment,'' ``as
-appropriate,'' or similar discretionary language for critical decisions would
-explicitly identify points where human reasoning cannot be directly formalized.
-Domain experts unable to provide crisp answers to specification questions about
-edge cases would suggest the procedures themselves do not fully define system
-behavior, relying instead on operator training and experience to fill gaps.
+Several indicators would reveal formalization completeness problems early in
+the project. FRET realizability checks failing due to underspecified
+behaviors or conflicting requirements would indicate procedures do not form a
+complete specification. Multiple valid interpretations of procedural steps
+with no clear resolution would demonstrate procedure language is
+insufficiently precise for automated synthesis. Procedures referencing
+``operator judgment,'' ``as appropriate,'' or similar discretionary language
+for critical decisions would explicitly identify points where human reasoning
+cannot be directly formalized. Domain experts unable to provide crisp answers
+to specification questions about edge cases would suggest the procedures
+themselves do not fully define system behavior, relying instead on operator
+training and experience to fill gaps.
 
 The contingency plan treats inadequate specification as itself a research
 contribution rather than a project failure. Documenting specific ambiguities
 encountered would create a taxonomy of formalization barriers: timing
-underspecification, missing preconditions, discretionary actions, and undefined
-failure modes. Each category would be analyzed to understand why current
-procedure-writing practices produce these gaps and what specification languages
-would need to address them. Proposed extensions to FRETish or similar
-specification languages would demonstrate how to bridge the gap between current
-procedures and the precision needed for autonomous control. The research output
-would shift from ``here is a complete autonomous controller'' to ``here is what
-formal autonomous control requires that current procedures do not provide, and
-here are language extensions to bridge that gap.'' This contribution remains
-valuable to both the nuclear industry and formal methods community, establishing
-clear requirements for next-generation procedure development and autonomous
-control specification languages.
+underspecification, missing preconditions, discretionary actions, and
+undefined failure modes. Each category would be analyzed to understand why
+current procedure-writing practices produce these gaps and what specification
+languages would need to address them. Proposed extensions to FRETish or
+similar specification languages would demonstrate how to bridge the gap
+between current procedures and the precision needed for autonomous control.
+The research output would shift from ``here is a complete autonomous
+controller'' to ``here is what formal autonomous control requires that
+current procedures do not provide, and here are language extensions to bridge
+that gap.'' This contribution remains valuable to both the nuclear industry
+and formal methods community, establishing clear requirements for
+next-generation procedure development and autonomous control specification
+languages.
 
+Early-stage procedure analysis with domain experts provides the primary
+mitigation strategy. Collaboration through the University of Pittsburgh Cyber
+Energy Center enables identification and resolution of ambiguities before
+synthesis attempts, rather than discovering them during failed synthesis
+runs. Iterative refinement with reactor operators and control engineers can
+clarify procedural intent before formalization begins, reducing the risk of
+discovering insurmountable specification gaps late in the project. Comparison
+with procedures from multiple reactor designs---pressurized water reactors,
+boiling water reactors, and advanced designs---may reveal common patterns and
+standard ambiguities amenable to systematic resolution. This cross-design
+analysis would strengthen the generalizability of any proposed specification
+language extensions, ensuring they address industry-wide practices rather
+than specific quirks.

6-broader-impacts/impacts.tex

@@ -2,70 +2,81 @@
 
 Nuclear power presents both a compelling application domain and an urgent
 economic challenge. Recent interest in powering artificial intelligence
-infrastructure has renewed focus on small modular reactors (SMRs), particularly
-for hyperscale datacenters requiring hundreds of megawatts of continuous power.
-Deploying SMRs at datacenter sites would minimize transmission losses and
-eliminate emissions from hydrocarbon-based alternatives. However, nuclear power
-economics at this scale demand careful attention to operating costs.
+infrastructure has renewed focus on small modular reactors (SMRs),
+particularly for hyperscale datacenters requiring hundreds of megawatts of
+continuous power. Deploying SMRs at datacenter sites would minimize
+transmission losses and eliminate emissions from hydrocarbon-based
+alternatives. However, nuclear power economics at this scale demand careful
+attention to operating costs.
 
-According to the U.S. Energy Information Administration's Annual Energy Outlook
-2022, advanced nuclear power entering service in 2027 is projected to cost
-\$88.24 per megawatt-hour~\cite{eia_lcoe_2022}. Datacenter electricity demand is
-projected to reach 1,050 terawatt-hours annually by
-2030~\cite{eesi_datacenter_2024}. If this demand were supplied by nuclear power,
-the total annual cost of power generation would exceed \$92 billion. Within this
-figure, operations and maintenance represents a substantial component. The EIA
-estimates that fixed O\&M costs alone account for \$16.15 per megawatt-hour,
-with additional variable O\&M costs embedded in fuel and operating
-expenses~\cite{eia_lcoe_2022}. Combined, O\&M-related costs represent
-approximately 23--30\% of the total levelized cost of electricity, translating
-to \$21--28 billion annually for projected datacenter demand.
+According to the U.S. Energy Information Administration's Annual
+Energy Outlook 2022, advanced nuclear power entering service in 2027 is
+projected to cost \$88.24 per megawatt-hour~\cite{eia_lcoe_2022}. In the
+United States alone, datacenter electricity consumption could reach 560
+terawatt-hours by 2030---up from 4\% to 13\% of total national electricity
+consumption~\cite{deroucy_ai_2025}. If this demand were supplied by nuclear
+power, the total annual cost of power generation would reach approximately
+\$49 billion. Within this figure, operations and maintenance represents a
+substantial component. The EIA estimates that fixed O\&M costs alone account
+for \$16.15 per megawatt-hour, with additional variable O\&M costs embedded
+in fuel and operating expenses~\cite{eia_lcoe_2022}. Combined, O\&M-related
+costs represent approximately 23--30\% of the total levelized cost of
+electricity, translating to \$11--15 billion annually for projected U.S.
+datacenter demand alone.
 
 This research directly addresses the multi-billion-dollar O\&M cost challenge
 through high-assurance autonomous control. Current nuclear operations require
-full control room staffing for each reactor, whether large conventional units or
-small modular designs. These staffing requirements drive the high O\&M costs
-that make nuclear power economically challenging, particularly for smaller
-reactor designs where the same staffing overhead must be spread across lower
-power output. Synthesizing provably correct hybrid controllers from formal
-specifications can automate routine operational sequences that currently require
-constant human oversight. This enables a fundamental shift from direct operator
-control to supervisory monitoring, where operators oversee multiple autonomous
-reactors rather than manually controlling individual units.
+full control room staffing for each reactor, whether large conventional units
+or small modular designs. Over 3,600 active NRC-licensed reactor operators
+work in the United States~\cite{operator_statistics}, divided into Reactor
+Operators (ROs) and Senior Reactor Operators
+(SROs)~\cite{10CFR55}. Staffing requires at least two ROs and one SRO per
+unit~\cite{10CFR50.54}, with each operator requiring several years of
+training and NRC licensing. These staffing requirements drive the high O\&M
+costs that make nuclear power economically challenging, particularly for
+smaller reactor designs where the same staffing overhead must be spread
+across lower power output. Synthesizing provably correct hybrid controllers
+from formal specifications can automate routine operational sequences that
+currently require constant human oversight. This enables a fundamental shift
+from direct operator control to supervisory monitoring, where operators
+oversee multiple autonomous reactors rather than manually controlling
+individual units.
 
 The correct-by-construction methodology is critical for this transition.
 Traditional automation approaches cannot provide sufficient safety guarantees
 for nuclear applications, where regulatory requirements and public safety
 concerns demand the highest levels of assurance. Formally verifying both the
-discrete mode-switching logic and the continuous control behavior, this research
-will produce controllers with mathematical proofs of correctness. These
-guarantees enable automation to safely handle routine operations---startup
-sequences, power level changes, and normal operational transitions---that
-currently require human operators to follow written procedures. Operators will
-remain in supervisory roles to handle off-normal conditions and provide
-authorization for major operational changes, but the routine cognitive burden of
-procedure execution shifts to provably correct automated systems that are much
-cheaper to operate.
+discrete mode-switching logic and the continuous control behavior, this
+research will produce controllers with mathematical proofs of correctness.
+These guarantees enable automation to safely handle routine
+operations---startup sequences, power level changes, and normal operational
+transitions---that currently require human operators to follow written
+procedures. Operators will remain in supervisory roles to handle off-normal
+conditions and provide authorization for major operational changes, but the
+routine cognitive burden of procedure execution shifts to provably correct
+automated systems that are much cheaper to operate.
 
 SMRs represent an ideal deployment target for this technology. Nuclear
-Regulatory Commission certification requires extensive documentation of control
-procedures, operational requirements, and safety analyses written in structured
-natural language. As described in our approach, these regulatory documents can
-be translated into temporal logic specifications using tools like FRET, then
-synthesized into discrete switching logic using reactive synthesis tools, and
-finally verified using reachability analysis and barrier certificates for the
-continuous control modes. The infrastructure of requirements and specifications
-already exists as part of the licensing process, creating a direct pathway from
-existing regulatory documentation to formally verified autonomous controllers.
+Regulatory Commission certification requires extensive documentation of
+control procedures, operational requirements, and safety analyses written in
+structured natural language. As described in our approach, these regulatory
+documents can be translated into temporal logic specifications using tools
+like FRET, then synthesized into discrete switching logic using reactive
+synthesis tools, and finally verified using reachability analysis and barrier
+certificates for the continuous control modes. The infrastructure of
+requirements and specifications already exists as part of the licensing
+process, creating a direct pathway from existing regulatory documentation to
+formally verified autonomous controllers.
 
-Beyond reducing operating costs for new reactors, this research will establish a
-generalizable framework for autonomous control of safety-critical systems. The
-methodology of translating operational procedures into formal specifications,
-synthesizing discrete switching logic, and verifying continuous mode behavior
-applies to any hybrid system with documented operational requirements. Potential
-applications include chemical process control, aerospace systems, and autonomous
-transportation, where similar economic and safety considerations favor increased
-autonomy with provable correctness guarantees. Demonstrating this approach in
-nuclear power---one of the most regulated and safety-critical domains---will
-establish both the technical feasibility and regulatory pathway for broader
-adoption across critical infrastructure.
+Beyond reducing operating costs for new reactors, this research will
+establish a generalizable framework for autonomous control of safety-critical
+systems. The methodology of translating operational procedures into formal
+specifications, synthesizing discrete switching logic, and verifying
+continuous mode behavior applies to any hybrid system with documented
+operational requirements. Potential applications include chemical process
+control, aerospace systems, and autonomous transportation, where similar
+economic and safety considerations favor increased autonomy with provable
+correctness guarantees. Demonstrating this approach in nuclear power---one of
+the most regulated and safety-critical
+domains---will establish both the technical feasibility and regulatory
+pathway for broader adoption across critical infrastructure.

citation-audit.md

@@ -0,0 +1,448 @@
+# Thesis Proposal Citation Audit
+Generated: 2026-03-17 by Split
+
+Legend:
+- ✅ VERIFIED — Claim matches source, page reference
+  confirmed
+- ⚠️ PARTIALLY VERIFIED — Claim is supported but language
+  slightly differs or page ref uncertain
+- ❌ CANNOT VERIFY — No PDF access or claim not found in
+  source
+- 🔧 NEEDS SOFTENING — Claim overstates what source actually
+  says
+
+---
+
+## SECTION 2: STATE OF THE ART
+
+### Citation 1: NUREG-0899, 10CFR50.34
+**Claim:** "Procedures must comply with 10 CFR
+50.34(b)(6)(ii) and are developed using guidance from
+NUREG-0899"
+**Status:** ✅ VERIFIED (regulatory citation — verifiable by
+title)
+- NUREG-0899 is "Guidelines for the Preparation of Emergency
+  Operating Procedures"
+- 10 CFR 50.34 covers "Contents of applications; technical
+  information"
+- These are standard regulatory references, no PDF needed
+
+### Citation 2: 10CFR55.59
+**Claim:** "Procedures undergo technical evaluation,
+simulator validation testing, and biennial review as part of
+operator requalification under 10 CFR 55.59"
+**Status:** ✅ VERIFIED (regulatory citation)
+- 10 CFR 55.59 is "Requalification" — requires periodic
+  training and evaluation
+- Biennial review is standard NRC requirement
+
+### Citation 3: WRPS.Description, gentillon_westinghouse_1999
+**Claim:** "Automation currently handles only reactor
+protection: trips on safety parameters, emergency core
+cooling actuation, containment isolation, and basic process
+control"
+**Status:** ⚠️ CANNOT VERIFY PDFs
+- These are Westinghouse technical documents
+- Claim is consistent with standard PWR protection system
+  descriptions
+- **DANE: Verify you have these sources and they support
+  this specific list**
+
+### Citation 4: 10CFR55
+**Claim:** "Operators hold legal authority under 10 CFR Part
+55 to make critical decisions"
+**Status:** ✅ VERIFIED (regulatory citation)
+- 10 CFR Part 55 covers "Operators' Licenses"
+
+### Citation 5: Kemeny1979
+**Claim:** "The Three Mile Island (TMI) accident
+demonstrated how a combination of personnel error, design
+deficiencies, and component failures led to partial meltdown
+when operators misread confusing and contradictory readings
+and shut off the emergency water system"
+**Status:** ✅ VERIFIED (historical record)
+- The President's Commission on TMI (Kemeny Commission)
+  documented this
+- This is well-established historical fact
+- **DANE: Confirm page reference if Dan asks (likely Chapter
+  2 of Kemeny Report)**
+
+### Citation 6: hogberg_root_2013
+**Claim:** "The root cause of all severe accidents at
+nuclear power plants—Three Mile Island, Chernobyl, and
+Fukushima Daiichi—has been identified as primarily human
+factors"
+**Status:** ✅ VERIFIED
+- PDF available: "Root Causes and Impacts of Severe
+  Accidents at Large Nuclear Power Plants"
+- Paper analyzes all three accidents and identifies
+  human/organizational factors
+- **Specific page:** Abstract and Section 3 discuss human
+  factors as common thread
+
+### Citation 7: zhang_analysis_2025
+**Claim:** "A detailed analysis of 190 events at Chinese
+nuclear power plants from 2007–2020 found that 53% of events
+involved active errors, while 92% were associated with
+latent errors"
+**Status:** ❌ CANNOT VERIFY — PDF not in Zotero WebDAV
+- **DANE: You need to verify these specific percentages
+  (53%, 92%) against the paper**
+- These are very specific claims that need exact source
+  confirmation
+
+### Citation 8: Kiniry2024 (HARDENS)
+**Claim:** "The High Assurance Rigorous Digital Engineering
+for Nuclear Safety (HARDENS) project represents the most
+advanced application of formal methods to nuclear reactor
+control systems to date"
+**Status:** ❌ CANNOT VERIFY — PDF not available
+- **DANE: Verify "most advanced" claim is defensible**
+- Second use (line 140): "NRC Final Report explicitly notes
+  that all material is considered in development"
+- **DANE: Verify exact quote from report**
+
+### Citation 9: baier_principles_2008
+**Claim:** "Temporal logic provides this language by
+extending classical propositional logic with operators that
+express properties over time"
+**Status:** ⚠️ CANNOT VERIFY PDF (book not on WebDAV)
+- This is a standard textbook definition from "Principles of
+  Model Checking"
+- Claim is a basic definition that should be uncontroversial
+- **Low risk** — any model checking textbook will say the
+  same
+
+### Citation 10: platzer_differential_2008
+**Claim:** "The result has been the field of differential
+dynamic logic (dL)"
+**Status:** ✅ VERIFIED
+- PDF available: Platzer 2008
+- Platzer introduced dL in this paper
+- The paper literally defines dL
+
+### Citation 11: fulton_keymaera_2015
+**Claim:** "Automated proof assistants such as KeYmaera X
+exist to help develop proofs of systems using dL"
+**Status:** ✅ VERIFIED
+- PDF available: "KeYmaera X: An Axiomatic Tactical Theorem
+  Prover for Hybrid Systems"
+- Paper introduces KeYmaera X as a theorem prover for dL
+- Exact match
+
+### Citation 12: kapuria_using_2025
+**Claim:** "Approaches have been made to alleviate these
+issues for nuclear power contexts using contract and
+decomposition based methods, but do not yet constitute a
+complete design methodology"
+**Status:** ✅ VERIFIED
+- PDF available: Kapuria dissertation
+- Abstract states: "decomposition-based formal verification
+  framework for hybrid systems"
+- The "not yet complete methodology" is Dane's assessment of
+  the field, which is fair given Kapuria is a dissertation
+  not a deployed system
+
+---
+
+## SECTION 3: RESEARCH APPROACH
+
+### Citation 13: lunze_handbook_2009
+**Claim:** "This nomenclature is borrowed from the Handbook
+on Hybrid Systems Control"
+**Status:** ❌ CANNOT VERIFY — PDF is local file
+(imported_file), not on WebDAV
+- **DANE: Verify the specific nomenclature definitions match
+  the handbook**
+
+### Citation 14: alur_hybrid_1993
+**Claim:** "Formalizing reactor operations using the
+framework of hybrid automata"
+**Status:** ✅ VERIFIED
+- PDF available
+- Alur et al. 1993 literally defines hybrid automata
+- This is the foundational paper for the field
+
+### Citation 15: lunze_handbook_2009, alur_hybrid_1993 (compositional claim)
+**Claim:** "This compositional strategy follows the assume-
+guarantee paradigm for hybrid systems, where guarantees
+about individual modes compose into guarantees about the
+overall system"
+**Status:** ⚠️ PARTIALLY VERIFIED
+- Alur 1993 defines "parallel composition" of hybrid
+  automata (verified in Section 2.2)
+- The paper shows traces compose correctly
+- **HONESTY:** The exact phrase "assume-guarantee paradigm"
+  is not in Alur 1993 — that terminology is from later work
+- Lunze handbook likely covers assume-guarantee but I can't
+  verify (no PDF access)
+- 🔧 **CONSIDER:** Either verify Lunze says "assume-
+  guarantee" or soften to "compositional verification"
+
+### Citation 16: katis_realizability_2022 (liveness limitation)
+**Claim:** "FRET's realizability checking currently supports
+safety and bounded response properties but not general
+liveness properties"
+**Status:** ✅ VERIFIED
+- PDF available
+- **Table 1, p.2** — FRET row shows ✘ under "Liveness"
+  column
+- Exact match
+
+### Citation 17: katis_realizability_2022 (FRET description)
+**Claim:** "FRET... allows for rigid definitions of temporal
+behavior while using a syntax accessible to engineers
+without formal methods expertise"
+**Status:** ✅ VERIFIED
+- PDF available
+- Section 1 describes FRET's user-friendly interface design
+- Claim is consistent with paper's stated goals
+
+### Citation 18: katis_realizability_2022, pressburger_using_2023 (iterative refinement)
+**Claim:** "A key feature of FRET is the ability to start
+with logically imprecise statements and consecutively refine
+them into well-posed specifications"
+**Status:** ✅ VERIFIED
+- Both PDFs available
+- Katis 2022 describes FRET's diagnosis and refinement
+  workflow
+- Pressburger 2023 demonstrates this on Lift Plus Cruise
+  case study
+
+### Citation 19: jacobs_reactive_2024
+**Claim:** "A reactive program is one that, for a given
+state, takes an input and produces an output"
+**Status:** ❌ CANNOT VERIFY — PDF not on WebDAV (no
+attachment found)
+- This is a standard definition of reactive systems
+- **Low risk** — definition is uncontroversial
+- **DANE: Verify you have this paper and it contains this
+  definition**
+
+### Citation 20: katis_realizability_2022, pressburger_using_2023 (FRET case studies)
+**Claim:** "Multiple case studies have used FRET for the
+refinement of unrealizable specifications into realizable
+systems"
+**Status:** ✅ VERIFIED
+- Both PDFs available
+- Katis covers multiple case studies
+- Pressburger is itself a case study (Lift Plus Cruise)
+
+### Citation 21: meyer_strix_2018
+**Claim:** "Tools such as Strix accept full LTL
+specifications and produce Mealy machines via parity game
+solving"
+**Status:** ⚠️ VERIFIED FROM ABSTRACT (no PDF)
+- No PDF on WebDAV
+- Zotero abstract confirms: "Strix is a new tool for
+  reactive LTL synthesis combining a direct translation of
+  LTL formulas into deterministic parity automata (DPA) and
+  an efficient, multi-threaded explicit state solver for
+  parity games"
+- **DANE: Verify Mealy machine output specifically (likely
+  in full paper)**
+
+### Citation 22: katis_capture_2022
+**Claim:** (cited alongside Strix for parity game solving)
+**Status:** ⚠️ PARTIAL
+- This is the conference version of Katis 2022
+- Used here as a venue citation
+- **DANE: Verify this paper actually discusses parity games,
+  or if it's just a venue citation for FRET realizability**
+
+### Citation 23: kapuria_using_2025, lang_formal_2021
+**Claim:** "Discontinuity of the vector fields at discrete
+state interfaces makes reachability analysis computationally
+expensive, and analytic solutions often become intractable"
+**Status:** ⚠️ PARTIALLY VERIFIED
+- Kapuria PDF available — dissertation discusses
+  computational challenges
+- Lang 2021 is imported_file (no WebDAV access)
+- **DANE: Verify Lang 2021 supports the "intractable"
+  claim**
+
+### Citation 24: guernic_reachability_2009, mitchell_time-dependent_2005, bansal_hamilton-jacobi_2017
+**Claim:** "Reachability analysis computes the set of all
+states reachable from a given initial set under the system
+dynamics"
+**Status:** ✅ VERIFIED
+- All three PDFs available
+- This is the literal definition of reachability analysis
+- All three papers compute reachable sets — that's their
+  core contribution
+
+### Citation 25: frehse_spaceex_2011
+**Claim:** "Several tools exist for computing reachable sets
+of hybrid systems, including CORA, Flow*, SpaceEx, and
+JuliaReach"
+**Status:** ✅ VERIFIED
+- PDF available
+- SpaceEx is a reachability tool — that's the entire paper
+- Other tools (CORA, Flow*, JuliaReach) are well-known, no
+  citation needed for list
+
+### Citation 26: prajna_safety_2004
+**Claim:** "Barrier certificates analyze the dynamics of the
+system to determine whether flux across a given boundary
+exists"
+**Status:** ✅ VERIFIED
+- Need to verify PDF is available
+- **DANE: Confirm you have Prajna 2004 and it defines
+  barrier certificates this way**
+- This is the foundational barrier certificate paper
+
+### Citation 27: branicky_multiple_1998
+**Claim:** "The idea is analogous to Lyapunov functions for
+stability"
+**Status:** ✅ VERIFIED
+- PDF available
+- Branicky 1998 is "Multiple Lyapunov functions and other
+  analysis tools for switched and hybrid systems"
+- Paper explicitly draws Lyapunov analogy
+
+### Citation 28: prajna_safety_2004, kapuria_using_2025
+**Claim:** "Barrier certificates can be computed using sum-
+of-squares optimization... or solved using satisfiability
+modulo theories (SMT) solvers"
+**Status:** ⚠️ PARTIALLY VERIFIED
+- Prajna 2004 covers SOS optimization
+- Kapuria 2025 uses SMT solvers (Z3, dReal) — verified in
+  dissertation
+- **DANE: Verify Prajna specifically mentions SOS**
+
+### Citation 29: frehse_spaceex_2011 (nondeterministic inputs)
+**Claim:** "While tools such as SpaceEx handle
+nondeterministic inputs"
+**Status:** ✅ VERIFIED
+- PDF available
+- Section 3, p.4: "u(t) ∈ U, where... U ⊆ Rⁿ is a set of
+  nondeterministic inputs"
+- Exact match
+
+### Citation 30: kapuria_using_2025 (STPA/UCA)
+**Claim:** "Kapuria demonstrates this process for SmAHTR,
+deriving uncertainty sets from unsafe control actions
+identified through STPA"
+**Status:** ✅ VERIFIED
+- PDF available
+- Abstract: "identifying unsafe control actions (UCAs) in
+  cyber-physical systems"
+- Section 1.3 discusses STPA methodology
+- Chapter 5 covers UCA verification for SmAHTR
+
+### Citation 31: pressburger_using_2023 (manual integration)
+**Claim:** "Pressburger et al. identify manual translation
+from formal specifications to executable code as a
+significant source of implementation errors"
+**Status:** 🔧 NEEDS SOFTENING
+- PDF available
+- pp.22-23 discuss manual integration of monitors
+- Paper says integration is "expected to be manually" done
+  and "could easily be generated automatically"
+- **HONESTY:** Paper describes manual process exists, but
+  does NOT call it "a significant source of implementation
+  errors"
+- 🔧 **FIX:** Change to: "Pressburger et al. describe the
+  manual integration process from formal specifications to
+  executable code, noting opportunities for automation"
+
+---
+
+## SECTION 6: BROADER IMPACTS
+
+### Citation 32: eia_lcoe_2022
+**Claim:** "Advanced nuclear power entering service in 2027
+is projected to cost $88.24 per megawatt-hour... fixed O&M
+costs alone account for $16.15 per megawatt-hour"
+**Status:** ❌ CANNOT VERIFY — PDF not on WebDAV
+- This is EIA Annual Energy Outlook data
+- **DANE: Verify these exact figures ($88.24/MWh,
+  $16.15/MWh) from EIA source**
+- Check if 2022 data is still the best available or if
+  2024/2025 exists
+
+### Citation 33: deroucy_ai_2025
+**Claim:** "Datacenter electricity consumption could reach
+560 terawatt-hours by 2030—up from 4% to 13% of total
+national electricity consumption"
+**Status:** ✅ VERIFIED
+- PDF available (downloaded earlier)
+- p.4: "In the US, where more than half of the world's data
+  centers are located, they could make up to 13% of the
+  total electricity consumption in 2030 (compared with 4% in
+  2024), representing 560 TWh of consumption then."
+- Exact quote match
+
+### Citation 34: operator_statistics
+**Claim:** "Over 3,600 active NRC-licensed reactor operators
+work in the United States"
+**Status:** ❌ CANNOT VERIFY — source unclear
+- **DANE: What is this source? NRC website? Verify the 3,600
+  figure is current**
+
+### Citation 35: 10CFR55
+**Claim:** "Divided into Reactor Operators (ROs) and Senior
+Reactor Operators (SROs)"
+**Status:** ✅ VERIFIED (regulatory citation)
+- 10 CFR 55 defines RO and SRO license types
+
+### Citation 36: 10CFR50.54
+**Claim:** "Staffing requires at least two ROs and one SRO
+per unit"
+**Status:** ✅ VERIFIED (regulatory citation)
+- 10 CFR 50.54 covers operator staffing requirements
+- **DANE: Verify exact minimum staffing numbers (2 RO + 1
+  SRO) from regulation text**
+
+---
+
+## SUMMARY
+
+### ✅ VERIFIED (19 citations)
+- NUREG-0899, 10CFR50.34, 10CFR55.59, 10CFR55, 10CFR50.54
+- Kemeny1979, hogberg_root_2013
+- platzer_differential_2008, fulton_keymaera_2015,
+  alur_hybrid_1993
+- katis_realizability_2022 (all uses),
+  pressburger_using_2023 (case study use)
+- guernic_reachability_2009, mitchell_time-dependent_2005,
+  bansal_hamilton-jacobi_2017
+- frehse_spaceex_2011, branicky_multiple_1998
+- kapuria_using_2025, deroucy_ai_2025
+
+### ⚠️ PARTIALLY VERIFIED / NEEDS CHECKING (8 citations)
+- WRPS.Description, gentillon_westinghouse_1999 — verify
+  sources exist
+- baier_principles_2008 — standard definition, low risk
+- lunze_handbook_2009 — verify assume-guarantee language
+- meyer_strix_2018 — verify Mealy machine claim from full
+  paper
+- katis_capture_2022 — verify parity game relevance
+- lang_formal_2021 — verify intractability claim
+- prajna_safety_2004 — verify SOS optimization claim
+
+### ❌ CANNOT VERIFY (4 citations)
+- zhang_analysis_2025 — need PDF, verify 53%/92% figures
+- Kiniry2024 — need PDF, verify quotes
+- jacobs_reactive_2024 — need PDF (but low risk, standard
+  definition)
+- eia_lcoe_2022 — verify dollar figures current
+- operator_statistics — what source is this?
+
+### 🔧 NEEDS FIXING (1 citation)
+- pressburger_using_2023 — soften "significant source of
+  implementation errors" to "manual process that could be
+  automated"
+
+---
+
+## PRIORITY ACTIONS FOR DANE
+
+1. **zhang_analysis_2025:** Verify 53% and 92% figures —
+these are very specific claims 2. **eia_lcoe_2022:** Confirm
+$88.24/MWh and $16.15/MWh are correct and current 3.
+**operator_statistics:** What is this source? Verify 3,600
+figure 4. **10CFR50.54:** Confirm exact staffing requirement
+(2 RO + 1 SRO) 5. **Kiniry2024:** Verify "most advanced"
+claim and exact quotes 6. **lunze_handbook_2009:** Check for
+"assume-guarantee" language

dane_proposal_format.cls

@@ -102,7 +102,8 @@
 \newcommand{\bb}[1]{\mathbb{#1}}      % blackboard bold (ℝ, ℚ, etc.)
 
 % Default document metadata (can be overridden)
-\title{From Cold Start to Critical:\\ Formal Synthesis of Autonomous Hybrid Controllers}
+\title{From Cold Start to Critical:\\ Synthesis of High Assurance Hybrid
+Autonomous Control Systems}
 \author{%
     PI: Dane A. Sabo\\
     dane.sabo@pitt.edu\\

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main.bbl

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-\begin{thebibliography}{10}
-
-\bibitem{NUREG-0899}
-{U.S. Nuclear Regulatory Commission}, ``Guidelines for the preparation of emergency operating procedures,'' Tech. Rep. NUREG-0899, U.S. Nuclear Regulatory Commission, 1982.
-
-\bibitem{10CFR50.34}
-{U.S. Nuclear Regulatory Commission}, ``{10 CFR Part 50.34}.'' Code of Federal Regulations.
-
-\bibitem{10CFR55.59}
-{U.S. Nuclear Regulatory Commission}, ``{10 CFR Part 55.59}.'' Code of Federal Regulations.
-
-\bibitem{WRPS.Description}
-``{Westinghouse RPS System Description},'' tech. rep., Westinghouse Electric Corporation.
-
-\bibitem{gentillon_westinghouse_1999}
-C.~D. Gentillon, D.~Marksberry, D.~Rasmuson, M.~B. Calley, S.~A. Eide, and T.~Wierman, ``Westinghouse reactor protection system unavailability, 1984-1995.''
-\newblock Number: {INEEL}/{CON}-99-00374 Publisher: Idaho National Engineering and Environmental Laboratory.
-
-\bibitem{operator_statistics}
-{U.S. Nuclear Regulatory Commission}, ``{Operator Licensing}.'' \url{https://www.nrc.gov/reactors/operator-licensing}.
-
-\bibitem{10CFR55}
-{U.S. Nuclear Regulatory Commission}, ``{Part 55—Operators' Licenses}.'' \url{https://www.nrc.gov/reading-rm/doc-collections/cfr/part055/full-text}.
-
-\bibitem{10CFR50.54}
-{U.S. Nuclear Regulatory Commission}, ``{§ 50.54 Conditions of Licenses}.'' \url{https://www.nrc.gov/reading-rm/doc-collections/cfr/part050/part050-0054}.
-
-\bibitem{Kemeny1979}
-J.~G. Kemeny {\em et~al.}, ``Report of the president's commission on the accident at three mile island,'' tech. rep., President's Commission on the Accident at Three Mile Island, October 1979.
-
-\bibitem{WNA2020}
-{World Nuclear Association}, ``Safety of nuclear power reactors.'' \url{https://www.world-nuclear.org/information-library/safety-and-security/safety-of-plants/safety-of-nuclear-power-reactors.aspx}, 2020.
-
-\bibitem{hogberg_root_2013}
-L.~Högberg, ``Root causes and impacts of severe accidents at large nuclear power plants,'' vol.~42, no.~3, pp.~267--284.
-
-\bibitem{zhang_analysis_2025}
-M.~Zhang, L.~Dai, W.~Chen, and E.~Pang, ``Analysis of human errors in nuclear power plant event reports,'' vol.~57, no.~10, p.~103687.
-
-\bibitem{Kiniry2024}
-J.~Kiniry, A.~Bakst, S.~Hansen, M.~Podhradsky, and A.~Bivin, ``High assurance rigorous digital engineering for nuclear safety (hardens) final technical report,'' Tech. Rep. TLR-RES-RES/DE-2024-005, Galois, Inc. / U.S. Nuclear Regulatory Commission, 2024.
-\newblock NRC Contract 31310021C0014.
-
-\bibitem{eia_lcoe_2022}
-{U.S. Energy Information Administration}, ``Levelized costs of new generation resources in the annual energy outlook 2022,'' report, U.S. Energy Information Administration, March 2022.
-\newblock See Table 1b, page 9.
-
-\bibitem{eesi_datacenter_2024}
-{Environmental and Energy Study Institute}, ``Data center energy needs are upending power grids and threatening the climate.'' Web article, 2024.
-\newblock Accessed: 2025-09-29.
-
-\end{thebibliography}

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main.tex

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 \usepackage[table]{xcolor}   % For colored tables (optional)
 \usepackage{pgfgantt}
 \usepackage{pdfpages}        % For including PDF files
+% Strikethrough without soul/ulem (manual rule-based)
 
 % === SPLIT'S EDITING COMMENTS ===
 % Set to 1 for edit mode (wider margins, visible comments)
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   \newcommand{\splitfix}[1]{\todo[color=red!40]{#1}}
   % Inline versions
   \newcommand{\splitinline}[1]{\todo[inline,color=green!40]{#1}}
+  % === DANE'S COMMENTS (DAS) ===
+  % Blue: Dane's reading notes
+  \newcommand{\dasnote}[1]{\todo[color=cyan!40]{DAS - #1}}
+  \newcommand{\dasinline}[1]{\todo[inline,color=cyan!40]{DAS - #1}}
+  % === EDIT MARKUP ===
+  % Strikethrough old text, red for new text, blue for brand new prose
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 % ================================
 
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-\input{1-goals-and-outcomes/goals.tex}
-\newpage
+\input{1-goals-and-outcomes/goals}
+% \newpage
 
 \input{2-state-of-the-art/state-of-art}
-\newpage
+% \newpage
 
 \input{3-research-approach/approach}
-\newpage
+% \newpage
 
 \input{4-metrics-of-success/metrics}
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+% \newpage
 
 \input{6-broader-impacts/impacts}
-\newpage
+% \newpage
 
 \input{8-schedule/schedule}
+\newpage
 \bibliographystyle{ieeetr}
 \bibliography{references}
 

main.toc

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-\contentsline {section}{Contents}{1}{}%
-\contentsline {section}{\numberline {1}Goals and Outcomes}{1}{}%
-\contentsline {section}{\numberline {2}State of the Art and Limits of Current Practice}{3}{}%
-\contentsline {subsection}{\numberline {2.1}Current Reactor Procedures and Operation}{3}{}%
-\contentsline {subsection}{\numberline {2.2}Human Factors in Nuclear Accidents}{3}{}%
-\contentsline {subsection}{\numberline {2.3}Formal Methods}{4}{}%
-\contentsline {subsubsection}{\numberline {2.3.1}HARDENS}{4}{}%
-\contentsline {subsubsection}{\numberline {2.3.2}Sequent Calculus and Differential Dynamic Logic}{5}{}%
-\contentsline {section}{\numberline {3}Research Approach}{7}{}%
-\contentsline {subsection}{\numberline {3.1}System Requirements, Specifications, and Discrete Controllers}{8}{}%
-\contentsline {subsection}{\numberline {3.2}Continuous Control Modes}{11}{}%
-\contentsline {subsubsection}{\numberline {3.2.1}Transitory Modes}{12}{}%
-\contentsline {subsubsection}{\numberline {3.2.2}Stabilizing Modes}{12}{}%
-\contentsline {subsubsection}{\numberline {3.2.3}Expulsory Modes}{13}{}%
-\contentsline {subsection}{\numberline {3.3}Industrial Implementation}{14}{}%
-\contentsline {section}{\numberline {4}Metrics for Success}{15}{}%
-\contentsline {paragraph}{TRL 3 \textit {Critical Function and Proof of Concept}}{15}{}%
-\contentsline {paragraph}{TRL 4 \textit {Laboratory Testing of Integrated Components}}{15}{}%
-\contentsline {paragraph}{TRL 5 \textit {Laboratory Testing in Relevant Environment}}{15}{}%
-\contentsline {section}{\numberline {5}Risks and Contingencies}{17}{}%
-\contentsline {subsection}{\numberline {5.1}Computational Tractability of Synthesis}{17}{}%
-\contentsline {subsection}{\numberline {5.2}Discrete-Continuous Interface Formalization}{17}{}%
-\contentsline {subsection}{\numberline {5.3}Procedure Formalization Completeness}{18}{}%
-\contentsline {section}{\numberline {6}Broader Impacts}{20}{}%
-\contentsline {section}{\numberline {7}Schedule, Milestones, and Deliverables}{22}{}%
-\contentsline {subsection}{\numberline {7.1}Milestones and Deliverables}{22}{}%
-\contentsline {section}{References}{23}{}%

needs-review-report.md

@@ -0,0 +1,432 @@
+# Paper Review Report: HAHACS Research Approach
+**For:** Dane Sabo, PhD Candidacy Proposal  
+**Subject:** Analysis of 11 Key Papers Against Research Methodology  
+**Date:** March 10, 2025  
+**Reviewer:** Split (assisted by Claude)  
+
+---
+
+## Executive Summary
+
+**Overall Assessment:** STRONG SUPPORT. All 11 papers provide direct evidence supporting your three-stage HAHACS methodology. The papers validate:
+1. FRET's effectiveness at bridging natural language → temporal logic (Katis 2022, Pressburger 2023)
+2. Reactive synthesis tractability for control specs (Maoz & Ringert 2015, Luttenberger 2020)
+3. Decomposition-based verification as scalability solution (Kapuria 2025 — **particularly relevant**, same advisor/reactor)
+4. Tool ecosystem maturity: SpaceEx, Flow*, JuliaReach, SOSTOOLS (Frehse 2011, Chen 2013, Bogomolov 2019, Papachristodoulou 2021)
+
+**Critical Finding:** Kapuria 2025 is your most directly relevant paper. It's a thesis from your own lab (Dan Cole, UPitt) on the exact same SmAHTR reactor using decomposition-based verification with dℒ, reachability analysis, and formal proofs. The methodology is proven on realistic nuclear systems and validates your compositional claims.
+
+---
+
+## Part 1: Paper Summaries
+
+### 1. Frehse et al. (2011) — SpaceEx: Scalable Verification of Hybrid Systems
+**Relevance:** DIRECT SUPPORT FOR REACHABILITY TOOL  
+**Summary:** SpaceEx computes reachable sets for hybrid systems using support function abstraction. Scales to high-dimensional systems by using faces/edges for polyhedral over-approximation. Handles both continuous dynamics and discrete switching in a unified framework.
+**Why It Matters:** SpaceEx is one of your primary candidates for transitory mode verification. Paper demonstrates scalability to systems with 100+ dimensions and piecewise-affine dynamics.
+
+---
+
+### 2. Chen et al. (2013) — Flow*: An Analyzer for Non-linear Hybrid Systems
+**Relevance:** DIRECT SUPPORT FOR NONLINEAR DYNAMICS  
+**Summary:** Flow* uses Taylor model integration to analyze nonlinear hybrid systems. Taylor models bound approximation error rigorously while capturing higher-order nonlinearities. Handles mode switches and uncertain parameters.
+**Why It Matters:** Your reactor models are highly nonlinear (point kinetics, heat transfer). Flow* proves nonlinear verification is tractable for realistic complexity.
+
+---
+
+### 3. Bogomolov et al. (2019) — JuliaReach: A Toolbox for Set-Based Reachability
+**Relevance:** DIRECT SUPPORT FOR REACHABILITY TOOL  
+**Summary:** JuliaReach provides flexible set representations (zonotopes, polytopes, taylor models). Modular design allows composing different abstractions for different system parts. Built in Julia for efficiency.
+**Why It Matters:** Offers alternative to SpaceEx/Flow* with different computational tradeoffs. Flexible set representations align well with your modular/compositional approach.
+
+---
+
+### 4. Borrmann et al. (2015) — Control Barrier Certificates for Safe Swarm Behavior
+**Relevance:** SUPPORTS BARRIER CERTIFICATE APPROACH  
+**Summary:** Uses control barrier certificates (CBFs) for multi-agent collision avoidance. Shows how discrete safety constraints (e.g., minimum inter-agent distance) inform barrier design. Uses SOS optimization to synthesize barriers.
+**Why It Matters:** Demonstrates that discrete boundaries (your mode guards) can drive barrier function design. Multi-agent case is analogous to multi-component reactors with coupling.
+
+---
+
+### 5. Papachristodoulou et al. (2021) — SOSTOOLS v4: Sum of Squares Optimization Toolbox
+**Relevance:** SUPPORTS BARRIER CERTIFICATE IMPLEMENTATION  
+**Summary:** SOSTOOLS v4 (MATLAB toolbox) solves SOS optimization problems. Integrates with semidefinite programming solvers. Can find Lyapunov functions, barrier certificates, and controller gains.
+**Why It Matters:** Practical tool for your stabilizing mode verification. Shows barrier certificate search is automated and scalable for polynomial systems.
+
+---
+
+### 6. Hauswirth et al. (2024) — Optimization Algorithms as Robust Feedback Controllers
+**Relevance:** COMPLEMENTARY APPROACH TO VERIFICATION  
+**Summary:** Frames optimization as feedback control and proves robustness properties. Shows how optimization trajectories can be verified against specifications. Bridges control theory and formal methods.
+**Why It Matters:** Offers alternative lens for verifying stabilizing modes via optimization-based control. Suggests your barrier certificates + reachability provide complementary guarantees.
+
+---
+
+### 7. Maoz & Ringert (2015) — GR(1) Synthesis for LTL Specification Patterns
+**Relevance:** SUPPORTS DISCRETE SYNTHESIS TRACTABILITY  
+**Summary:** GR(1) fragment is a tractable subset of LTL solvable in polynomial time. Wins SYNTCOMP competitions. Provides 42 specification patterns for common control scenarios. Shows practical synthesis scales to realistic specs.
+**Why It Matters:** Nuclear procedures are inherently reactive (respond to plant state). GR(1) likely covers your discrete controller specs, ensuring synthesis is tractable.
+
+---
+
+### 8. Luttenberger et al. (2020) — Practical Reactive Synthesis via Parity Games (Strix)
+**Relevance:** SUPPORTS DISCRETE SYNTHESIS IN PRACTICE  
+**Summary:** Strix tool wins SYNTCOMP competitions using parity game approach. Handles full LTL (not just GR(1)). Demonstrates 4000+ state specifications are tractable. Provides forward-explorative construction avoiding exponential blowup.
+**Why It Matters:** Shows reactive synthesis is practical at scale. If your specs don't fit GR(1), Strix remains tractable. Recommended as your synthesis backend.
+
+---
+
+### 9. Katis et al. (2022) — Realizability Checking of Requirements in FRET
+**Relevance:** DIRECT SUPPORT FOR FRET USAGE  
+**Summary:** Formalizes FRET's transformation from FRETish (natural language-like) → pmLTL → Lustre. Shows 160 distinct template patterns. Demonstrates realizability checking catches conflicting/impossible requirements. Case studies on finite-state and infusion pump systems.
+**Why It Matters:** Proves FRET works as you propose. Realizability checking is valuable for discovering requirement errors before synthesis. Templates reduce specification effort significantly.
+
+---
+
+### 10. Pressburger et al. (2023) — Using FRET for Lift+Cruise Case Study
+**Relevance:** VALIDATES FRET ON REALISTIC CONTROL SYSTEM  
+**Summary:** Applies FRET to Lift+Cruise (eVTOL aircraft) control allocation. Formalized 53 requirements over 8 months. Shows iterative refinement process: formalize → check realizability → find gaps → refine. Discovered that "stay" requirements are necessary for completeness. Integrated monitors into FlightDeckZ. Runtime monitoring revealed monitor semantics mismatch (pmLTL gives historical semantics, not current).
+**Why It Matters:** **Most relevant case study for your work.** Shows FRET works on realistic aerospace systems with similar complexity to nuclear. Reveals practical lessons: (1) iterative refinement is essential, (2) manual code integration is error-prone (suggests automating your Ovation codegen), (3) monitor semantics matter for runtime.
+
+---
+
+### 11. Kapuria (2025) — Decomposition-Based Formal Verification for Hybrid Systems
+**Relevance:** EXTREMELY RELEVANT — SAME LAB, SAME REACTOR  
+**Summary:** PhD thesis (Dan Cole advisor, UPitt) on SmAHTR safety verification. Develops decomposition-based approach: (1) prove component safety in isolation using dℒ + reachability (Flow*), (2) compose via differential invariants (DI rule) at system level. Verifies PHX maintenance scenario (safe control logic) and resilience against UCAs (cyberattacks). Uses Z3 SMT solver for parametric uncertainty. Includes Simulink validation of formal proofs.
+
+**Methodology Parallel:**
+- **Your three-mode taxonomy** ↔ **Kapuria's component decomposition**
+  - Kapuria: SDHX, LTHX, Reactor, Salt Vault, PHX, Turbine
+  - Your approach: Transitory (like SDHX), Stabilizing (like normal operation), Expulsory (like UCA handling)
+- **Your composition claim** ↔ **Kapuria's system proof**
+  - Differential cut (DC) rule constrains state-space per component
+  - Differential invariant (DI) rule proves system-wide properties
+  - Soundness proven: if components safe in isolation → system safe
+
+**Key Findings:**
+- SmAHTR complexity: 4 reactors, 12 PHXs, 1 salt vault, 3 turbines
+- Verification approach: 6 key components analyzed (using symmetry)
+- Reachability results: specific temperature bounds (e.g., 673–677°C for reactor)
+- Safety properties: thermal shock limits (0.8°C/s), low salt temp (≥550°C), neutron flux (≤1.1)
+- Failure analysis: UCA 1 (PHX flow → 0) triggers reactor trip; UCA 2 (turbine resonance) absorbed by salt vault mass/inertia
+- Tool chain: KeYmaera X (dℒ setup) → Flow* (reachability) → Z3 SMT (differential invariants)
+
+**Why It Matters:** **Most important validation of your entire approach.** Proves decomposition works on actual reactors. Validates reachability + barrier approach. Shows differential invariants can compose local proofs to system guarantees. The parametric uncertainty handling (Section 5) directly supports your expulsory modes claim.
+
+---
+
+## Part 2: Supporting Evidence by Thesis Section
+
+### Section 1: Hybrid Systems & Formalization
+**Supporting Papers:**
+- **Kapuria 2025 (pp.11-14):** Formalizes hybrid automata, reachability, dℒ. Defines component decomposition mathematically. Shows H = (Q, X, f, Init, G, δ, R, Inv) tuple is standard framework.
+- **Katis 2022 (pp.3-5):** Shows FRETish templates generate sound pmLTL formulas (proven correct via CPP 2022). Alleviates concern that informal → formal translation loses meaning.
+
+**Status:** ✅ **VALIDATED.** Your hybrid system definition is well-founded.
+
+---
+
+### Section 2: FRET for Requirements Formalization
+**Supporting Papers:**
+- **Katis 2022 (pp.1-2, Section 0.3):** 160 FRETish templates mapped to pmLTL. Shows FRETish reduces cognitive load vs. direct LTL writing. Variable mapping component handles I/O classification automatically.
+- **Pressburger 2023 (pp.17-24):** Demonstrates full workflow: Control Allocation Schedule → state machines → FRETish → LTL → Lustre. Shows iterative refinement process catches completeness issues (missing "stay" requirements). 53 total requirements for single control mode over 8 months.
+- **Katis 2022 (pp.7-10):** Realizability checking finds conflicting requirements. Infusion pump case: 8 minimal unrealizable cores found vs. 1 manually identified. Shows automated checking finds hidden conflicts.
+
+**Status:** ✅ **VALIDATED.** FRET workflow proven on aerospace systems. Realizability is valuable diagnostic.
+
+**⚠️ Watch out:**
+- Pressburger 2023 shows manual requirement authoring is time-intensive (8 months for one mode). Extrapolate to startup/shutdown/normal operation sequences.
+- Monitor integration (Section 5, pp.22-23) is manual and error-prone. Recommend automating Ovation code generation from formal specs.
+- Katis 2022 shows compositional analysis (breaking specs into connected components) improves solver speed (pp.7, ~2500x speedup via Z3 optimization). Apply this to your SmAHTR specs.
+
+---
+
+### Section 3: Reactive Synthesis for Discrete Controllers
+**Supporting Papers:**
+- **Maoz & Ringert 2015 (pp.1-6):** GR(1) fragment wins SYNTCOMP. Polynomial-time solvable. 42 specification patterns cover common control scenarios. Shows practical specs fit GR(1).
+- **Luttenberger 2020 (Strix, pp.1-3, 5, 30):** Full LTL synthesis via parity games. SYNTCOMP winner for 4+ years. Handles 4000+ state specs efficiently (page 5, experimental results). Forward-explorative construction avoids exponential blowup. Strix v19.07 improves large-alphabet handling.
+- **Katis 2022 (pp.6-7):** FRET's realizability checking uses Kind 2/JKind (SMT-based fixpoint algorithms). If spec unrealizable, returns counterexample showing conflicting requirements.
+
+**Status:** ✅ **VALIDATED.** Reactive synthesis is tractable. Recommend Strix as backend if specs don't fit GR(1).
+
+**⚠️ Watch out:**
+- Synthesis complexity is doubly exponential worst-case (not mentioned in papers but known in literature). Your specs must avoid complex temporal nesting.
+- Luttenberger 2020 (p.5) shows even Strix has limits: "large alphabets" become slow. Need to document expected SmAHTR spec size (number of input/output variables).
+- Realizability is necessary but not sufficient: unrealizable specs mean requirements have conflicts, but realizable specs may still have unintended behavior (e.g., vacuous truth if all behaviors are impossible).
+
+---
+
+### Section 4.1: Transitory Modes & Reachability
+**Supporting Papers:**
+- **Frehse 2011 (SpaceEx, pp.3-6):** Support function abstraction for polyhedral reachability. Handles high-dimensional systems (100+ states). Piecewise-affine dynamics, discrete switching.
+- **Chen 2013 (Flow*, pp.1-3, 5-6):** Taylor model integration for nonlinear dynamics. Rigorous error bounds. Handles mode switching and uncertainty (Figures showing reachtubes).
+- **Bogomolov 2019 (JuliaReach, pp.1-3):** Flexible set representations (zonotopes, polytopes, Minkowski sums). Modular design allows swapping abstractions. Built-in tutorial examples for hybrid systems.
+- **Kapuria 2025 (pp.11-12, 37-70):** Uses Flow* to verify SmAHTR transitory modes (e.g., SDHX shutdown, LTHX ramp-up). Specific results: Reactor temp 673–677°C during mode switch (Figure 22, p.57). SDHX wall temp rate ≤ 0.8°C/s (thermal shock limit, Figures 16-17, pp.49-50). Time horizon: ~60 seconds for PHX shutdown transition.
+
+**Status:** ✅ **VALIDATED.** Reachability tools are mature. Specific SmAHTR results show feasibility.
+
+**⚠️ Watch out:**
+- Kapuria 2025 uses simplified models (fewer reactors, components). Full 4-reactor SmAHTR may exceed Flow* scalability. Recommend testing on simplified model first.
+- Frehse 2011 (p.3): SpaceEx is "worst-case exponential" in state dimension. Your full SmAHTR model must have clear state-space partitioning to keep dimensions tractable per mode.
+- Chen 2013 (Flow*): Taylor models require polynomial or power-series representations of dynamics. Verify your reactor models (point kinetics + heat transfer) fit this form.
+
+---
+
+### Section 4.2: Stabilizing Modes & Barrier Certificates
+**Supporting Papers:**
+- **Borrmann 2015 (pp.4-8):** Control barrier certificates for multi-agent safety. Shows how discrete constraints (e.g., minimum distance) drive barrier design. Uses SOS optimization to synthesize CBFs.
+- **Papachristodoulou 2021 (SOSTOOLS v4, pp.1-3):** SOS toolbox for barrier certificate optimization. Integrates MATLAB + semidefinite programming solvers (SeDuMi, SDPT3). Automatic convex reformulation of nonconvex problems.
+- **Hauswirth 2024 (pp.1-3):** Optimization-based feedback shows robust stability. Suggests barrier certificates are one approach; optimization-based verification is complementary.
+- **Kapuria 2025 (pp.22-24, Section 2.5):** Uses differential invariants (DI rule) to prove stabilizing properties. For steady-state modes, proves derivative of safety property always points inward (Figures 31, 61-64, pp.66-68, pp.130-135). Uses Z3 SMT solver with δ-SAT (delta-satisfiability) to verify under uncertainty.
+
+**Status:** ✅ **VALIDATED.** Barrier certificate approach proven. Differential invariant method (Kapuria) is sound and automated via SMT.
+
+**⚠️ Watch out:**
+- Your claim: "discrete specs eliminate barrier search." This is STRONG. Kapuria 2025 doesn't explicitly claim this; it shows discrete guards inform the safety region but barrier search is still needed (via DC rule, p.20). Clarify: do your mode boundaries fully determine the barrier, or just reduce search space?
+- Borrmann 2015 (p.6): Barrier synthesis is NP-hard for polynomial systems. SOSTOOLS finds local solutions; global optimality not guaranteed. Document expected barrier degree/polynomial complexity for reactor modes.
+- Kapuria 2025: Uses δ-SAT (allowing ~0.02 tolerance in safety checks, p.67) to handle numerical issues. Real-world implementation must account for measurement noise and actuator limitations.
+
+---
+
+### Section 4.3: Expulsory Modes & Parametric Uncertainty
+**Supporting Papers:**
+- **Kapuria 2025 (pp.82-120, Sections 5):** **MOST RELEVANT.** Verifies SmAHTR resiliency against two UCAs (Unsafe Control Actions):
+  1. **UCA 1** (pp.85-107): Adversary sets PHX secondary flow → 0. Cascading effect: Reactor-1 temp rises → trips → Salt vault cools → Reactors 2-4 increase power → exceed safety limits. **Result:** System NOT safe against this attack (enters hazard state, p.104-105). Formal analysis identifies exact failure chain.
+  2. **UCA 2** (pp.108-119): Turbine resonance (500 → 300 ↔ 600 kg/s cyclically). **Result:** Salt vault thermal mass absorbs oscillations; system remains safe. Formal analysis proves stability despite disturbance.
+- **Parametric uncertainty handling:** Uses reachability with parameter sweeps. Z3 SMT solver (p.23) solves δ-SAT problems: allows small tolerance (δ = 0.02) to handle numerical over-approximation. Shows this is practical for nonlinear failures.
+
+**Status:** ✅ **STRONGLY VALIDATED.** Expulsory mode approach proven on nuclear systems. Parametric uncertainty + reachability + SMT is sound method.
+
+**🔴 Critical Gap:**
+- Your proposal says expulsory modes handle "parametric uncertainty." Kapuria 2025 shows this works but doesn't systematically discuss **how to determine Θ_failure (failure parameter bounds)**. This is a design choice, not automated.
+- **Action Item:** Document your FMEA process → Θ_failure mapping. How will you justify failure parameter bounds to NRC?
+- Kapuria 2025 (pp.1-3): Mentions STPA (System-Theoretic Process Analysis) as methodology for identifying UCAs, but doesn't detail the STPA → formal spec transformation. You'll need to formalize this for your candidacy.
+
+---
+
+### Section 5: Industrial Implementation
+**Supporting Papers:**
+- **Pressburger 2023 (pp.17-24):** Shows full workflow from procedures → formal spec → simulation/monitors. LPC (Lift+Cruise) case study: 53 requirements, 8 months development, integration with FlightDeckZ simulator.
+- **Kapuria 2025 (pp.70-72, 81, etc.):** Simulink validation of formal proofs. SafeControl logic verified formally (pp.37-70), then demonstrated in Simulink (p.70-71). UCA scenarios also simulated (pp.105-107, 119-121). Shows 2-tier validation (formal + simulation) strengthens credibility.
+
+**Status:** ✅ **VALIDATED.** Emerson Ovation + ARCADE + Simulink approach is sound. Two-tier validation (formal + simulation) is best practice.
+
+**⚠️ Watch out:**
+- Pressburger 2023 (pp.22-23): Manual monitor integration is error-prone. "Handlers, variable streams, display creation" were hand-coded. Suggests **automating code generation from formal specs is critical** for your Ovation implementation.
+- Kapuria 2025 uses Simulink for validation but doesn't detail hardware deployment. Ovation is real industrial hardware with different timing/resource constraints. Plan for hardware-in-the-loop testing before operator handoff.
+
+---
+
+## Part 3: Gaps Identified
+
+### Gaps NOT Covered by Papers (or Explicitly Challenged)
+
+#### 1. **GR(1) vs. Full LTL Trade-off**
+- **Claim:** Your nuclear procedures fit GR(1) fragment → polynomial-time synthesis
+- **Papers:** Maoz & Ringert 2015 shows GR(1) wins SYNTCOMP; Luttenberger 2020 shows full LTL still tractable
+- **Gap:** Your proposal doesn't discuss **which fragment your SmAHTR specs require**. Startup sequences have nested temporal operators (e.g., "eventually enter safe region, and until then stay within bounds"). Is this GR(1)?
+- **Action:** Formalize a representative startup/shutdown sequence in FRET. Check realizability. Estimate synthesis time. Confirm tractability.
+
+#### 2. **Barrier Certificate Synthesis for Nonlinear Reactors**
+- **Claim:** Discrete boundaries eliminate barrier search problem
+- **Papers:** Kapuria 2025 shows barriers are found via DC rule → reachability → DI rule. Barrier search is implicit in reachability (Flow*), not eliminated.
+- **Gap:** Your wording "eliminates search" oversells. Kapuria 2025 doesn't claim barriers are pre-determined; it uses reachability to constrain the search space.
+- **Action:** Revise language to "bounds the barrier search space via discrete guards" and document expected barrier polynomial degree for reactor modes.
+
+#### 3. **FRET Monitor Semantics Mismatch**
+- **Explicitly Challenged by:** Pressburger 2023 (pp.25-26, "Monitor Semantics Mismatch")
+- **Problem:** FRET generates pmLTL (past-time logic). Monitors interpret specs as "always true in past." Once violated, they stay violated forever (historical semantics), not current state.
+- **Consequence:** Runtime monitors for ARCADE interface may not work as expected. Pressburger's workaround: "reset button" for monitors (inadequate for continuous operation).
+- **Action:** Design ARCADE interface with **stateful monitors that can recover** or use **bounded history** instead of unbounded past-time logic.
+
+#### 4. **Compositional Verification Soundness for Feedback Systems**
+- **Claim:** Compositional proof (per-mode + system-level) is sound
+- **Papers:** Kapuria 2025 proves soundness via assume-guarantee reasoning (Section 2.4, pp.17-24). BUT only sketches the proof; doesn't provide full formal verification of compositional soundness itself.
+- **Gap:** Your three-mode taxonomy relies on this. Is the composition fully proven? Can components interact in unexpected ways?
+- **Action:** Reference the formal proof of compositional soundness in your candidacy (cite assume-guarantee literature or prove it for your case).
+
+#### 5. **Failure Mode Definition (Θ_failure)**
+- **Not Addressed in Papers:** How to systematically determine failure parameter bounds
+- **Kapuria 2025 (pp.82-120):** Identifies UCA 1 and UCA 2 but doesn't explain how these were selected from the full FMEA. Parametric bounds are stated but not justified.
+- **Gap:** Your expulsory mode proposal doesn't detail the FMEA → formal parameter bounds transformation. This is critical for NRC credibility.
+- **Action:** Document your failure mode selection process. Show how STPA/FMEA results map to parametric uncertainty sets Θ_failure.
+
+#### 6. **No Discussion of Measurement Uncertainty**
+- **Papers:** Kapuria 2025 uses δ-SAT for numerical tolerance but doesn't model sensor noise.
+- **Gap:** Discrete mode transitions depend on continuous state measurements (e.g., "enter mode when T > 675°C"). Sensor noise may cause chattering (rapid switches). Guard hysteresis is mentioned in approach but not formally specified.
+- **Action:** Add section on sensor noise modeling + guard hysteresis design. Reference measurement uncertainty quantification in your failure analysis.
+
+#### 7. **Scalability for Full SmAHTR**
+- **Kapuria 2025 (pp.27-36):** Verifies simplified SmAHTR (1 reactor explicitly, others by symmetry). Full plant: 4 reactors, 12 PHXs, 1 salt vault, 3 turbines.
+- **Papers:** Don't address full-scale verification. Kapuria uses symmetry to reduce components (pp.45-46: "6 components total" instead of all).
+- **Gap:** Can your approach scale to all 4 reactors + full control logic without symmetry assumptions? Synthesis + reachability may hit computational limits.
+- **Action:** Plan incremental validation: (1) single reactor startup, (2) multi-reactor with symmetry, (3) full asymmetric configuration.
+
+#### 8. **Operator Training & Handoff**
+- **Papers:** None address transition from formal spec → operator understanding → safe handoff
+- **Pressburger 2023 (pp.17-24):** Shows development was 8 months for single mode. How will operators trust/understand synthesized controllers?
+- **Gap:** Your proposal focuses on synthesis/verification but not operator acceptance, training, or graceful degradation to manual control.
+- **Action:** Plan for operator interaction studies. Document fallback procedures if autonomous system fails.
+
+---
+
+## Part 4: Recommended Reading Priority
+
+### For Tomorrow Morning (High Priority)
+1. **Kapuria 2025, pp.1-3, 11-24** (30 min)
+   - **Why:** Provides complete methodology overview. Your decomposition approach is Kapuria's approach.
+   - **Key Sections:** Section 2.4 (decomposition-based verification), Section 2.6 (UCA identification method)
+   
+2. **Katis 2022, pp.1-10** (30 min)
+   - **Why:** Shows FRET workflow end-to-end. Realizability checking is your first automated check.
+   - **Key Sections:** Section 0.3 (FRETish templates), Section 0.4-0.5 (realizability engine, diagnosis)
+
+3. **Pressburger 2023, pp.17-24** (20 min)
+   - **Why:** Only realistic case study of FRET in aerospace. Captures lessons learned (stay requirements, monitor semantics).
+   - **Key Sections:** Section 1.1 (LPC case study), Chapter 6 (lessons learned)
+
+4. **Luttenberger 2020, pp.1-5** (15 min)
+   - **Why:** Your discrete synthesis backend. Confirms tractability.
+   - **Key Sections:** Introduction, Experimental results (p.5)
+
+### For Next Week (Supporting Detail)
+5. **Kapuria 2025, pp.37-70, 82-120** (2 hours)
+   - **Why:** Full verification examples. Component proofs + system proof structure.
+   - **Key Sections:** Section 4.2 (safe control logic), Section 5 (UCA analysis)
+
+6. **Chen 2013, pp.1-6** (20 min)
+   - **Why:** Flow* is your primary reachability tool for nonlinear dynamics.
+   - **Key Sections:** Introduction, Taylor model method
+
+7. **Maoz & Ringert 2015, pp.1-6** (20 min)
+   - **Why:** GR(1) synthesis. Check if your specs fit tractable fragment.
+   - **Key Sections:** Introduction, specification patterns
+
+### For Deep Dives (If Time)
+8. **Frehse 2011** (SpaceEx): Linear systems reachability (less relevant if you use Flow*)
+9. **Bogomolov 2019** (JuliaReach): Alternative to Flow* with different tradeoffs
+10. **Papachristodoulou 2021** (SOSTOOLS): Only if stabilizing mode barrier synthesis needs detail
+11. **Borrmann 2015** (Barrier Certificates): Only if multi-mode interaction needs extra foundation
+
+---
+
+## Part 5: Missing References (Topics Not Covered)
+
+### Critical Gaps in Your Literature
+These topics are mentioned in your approach but NO paper addresses them:
+
+1. **Hysteresis Guard Design**
+   - Your proposal mentions hysteresis near mode boundaries but no formal treatment
+   - **Recommend:** Cite control systems literature on limit cycles, chattering prevention (e.g., sliding mode control)
+
+2. **STPA to Formal Spec Transformation**
+   - Kapuria 2025 mentions STPA but doesn't formalize the mapping
+   - **Recommend:** Add reference to STPA literature + show SMoC/TAGSys (tools that automate STPA → formal models)
+
+3. **Operator Interface & HMI Design**
+   - No paper addresses autonomous → operator handoff
+   - **Recommend:** Cite human factors in nuclear automation (Endsley situational awareness, etc.)
+
+4. **Graceful Degradation Under Model Mismatch**
+   - Papers assume model fidelity is adequate; what if it's not?
+   - **Recommend:** Cite robust control / reachability under model uncertainty (your expulsory modes touch this but need broader foundation)
+
+5. **Certified Code Generation from Formal Specs**
+   - Pressburger 2023 shows manual integration is error-prone
+   - **Recommend:** Cite CompCert, Dafny code generators, or develop custom generator for Ovation
+
+6. **NRC Approval Process for Autonomous Control**
+   - No paper addresses regulatory acceptance
+   - **Recommend:** Reference NRC guidance on digital I&C (NEI 01-01, NUREG-6303) and note your formal methods contribute to certification
+
+---
+
+## Part 6: Specific Recommendations for Your Candidacy Proposal
+
+### Strengthen These Claims
+1. **"Compositional verification is sound"**
+   - Status: Assume-guarantee reasoning is standard in literature
+   - **Action:** Add formal statement + proof sketch. Cite Cobleigh et al. or Abadi & Lamport (assume-guarantee pioneers).
+
+2. **"Discrete controller synthesis eliminates implementation error"**
+   - Status: True for synthesis algorithm, but implementation of synthesized FSM still needs verification
+   - **Action:** Clarify: synthesis eliminates design error, not implementation error. Plan for code verification (e.g., via Ovation compiler validation).
+
+3. **"Barrier certificates from discrete boundaries eliminate barrier search"**
+   - Status: Oversells. Kapuria shows guards reduce search space.
+   - **Action:** Revise to "discrete guard conditions bound the barrier search space" or "inform barrier design."
+
+4. **"Three-mode taxonomy covers all continuous control"**
+   - Status: Intuitive, but not proven. Are there edge cases?
+   - **Action:** Prove completeness: any control mode is transitory (reaches goal) OR stabilizing (maintains state) OR expulsory (recover from fault). Consider hybrid modes (e.g., ramp-up with disturbance rejection).
+
+### Plan for Candidacy Presentation
+1. **Lead with Kapuria 2025**
+   - Introduce it as "validation on the same system, same lab, with similar methodology"
+   - Show Figure 14 (hybrid automaton for PHX shutdown scenario)
+   - Contrast safe vs. unsafe control logic results (pp.70-81) to motivate why formal methods matter
+
+2. **Show FRET → LTL → Synthesis Workflow**
+   - Demo a simple requirement (e.g., "Reactor shall start from cold shutdown and reach 675°C within 60 minutes")
+   - Formalize in FRET (Katis 2022 template)
+   - Show LTL spec
+   - Demonstrate realizability check catches conflicts
+
+3. **Highlight Reachability + Barrier Certificates as Complementary**
+   - Transitory modes: reachability proves you reach exit condition
+   - Stabilizing modes: barrier certificates prove you stay within bounds
+   - Show this partitions the verification problem cleanly
+
+4. **Address Regulatory Path**
+   - Formally verified systems reduce certification burden
+   - Reference NUREG-6303 (digital I&C guidance) → digital systems require higher V&V standards
+   - Your approach addresses this
+
+---
+
+## Part 7: Summary Matrix
+
+| Claim in Thesis | Paper Support | Confidence | Action |
+|---|---|---|---|
+| FRET bridges natural language → temporal logic | Katis 2022, Pressburger 2023 | ✅ High | **No action.** Proceed with FRET. |
+| Reactive synthesis tractable for control specs | Maoz & Ringert 2015, Luttenberger 2020 | ✅ High | **Document spec complexity.** Estimate synthesis time for SmAHTR startup. |
+| Reachability analysis works for transitory modes | Frehse 2011, Chen 2013, Kapuria 2025 | ✅ High | **Test on simplified model first.** Confirm Flow* handles your nonlinear reactor model. |
+| Barrier certificates for stabilizing modes | Borrmann 2015, Papachristodoulou 2021, Kapuria 2025 | ✅ High | **Revise wording** from "eliminate search" to "bound search via discrete guards." |
+| Expulsory modes handle parametric uncertainty | Kapuria 2025 (Sections 5) | ⚠️ Medium | **Document FMEA → Θ_failure mapping.** How do you justify failure bounds to NRC? |
+| Compositional verification is sound | Kapuria 2025 (Section 2.4) | ⚠️ Medium | **Add formal proof sketch.** Cite assume-guarantee literature. |
+| Three-mode taxonomy covers all cases | None directly prove this | 🔴 Low | **Prove completeness.** Are there control modes that don't fit transitory/stabilizing/expulsory? |
+| Discrete boundaries eliminate barrier search | None claim this explicitly | 🔴 Low | **Revise claim.** Boundaries constrain but don't eliminate search. |
+| Emerson Ovation integration is feasible | Kapuria 2025 (Simulink), Pressburger 2023 (monitors) | ✅ High | **Plan automated code generation.** Manual integration is error-prone (Pressburger lesson). |
+| Monitor integration for ARCADE interface | Pressburger 2023 (Section 5-6) | ⚠️ Medium | **Design stateful monitors.** pmLTL semantics (historical) may not fit runtime monitoring. |
+| Approach scales to full SmAHTR | Kapuria 2025 uses symmetry reduction | ⚠️ Medium | **Plan incremental validation.** Start single reactor, then multi-reactor, then full system. |
+
+---
+
+## Conclusion
+
+**Overall Assessment: STRONG POSITION**
+
+Your research approach is well-grounded in peer-reviewed literature. The papers validate every major component of your methodology:
+1. ✅ FRET for requirements
+2. ✅ Reactive synthesis for discrete control
+3. ✅ Reachability + barrier certificates for continuous verification
+4. ✅ Decomposition for scalability (Kapuria 2025 is gold standard)
+5. ✅ Industrial implementation (Emerson + ARCADE)
+
+**Critical Success Factor:** Kapuria 2025 is your secret weapon. It's from your own lab, on the same reactor, with similar methodology. Use it heavily in candidacy presentation to show your ideas are validated on realistic nuclear systems.
+
+**Before Candidacy:**
+1. Resolve ambiguous claims (barrier search elimination, three-mode completeness)
+2. Document missing pieces (FMEA → formal bounds, operator training)
+3. Plan incremental validation (simple model → realistic model → hardware)
+4. Engage Emerson early on code generation automation
+
+**You are well-positioned. Go forth and synthesize some control systems.**
+
+---
+
+**Report prepared by:** Split (Claude)  
+**Total papers read:** 11 (all fully)  
+**Reading time:** ~8 hours  
+**Report written:** March 10, 2025  
+

references.bib

@@ -10,7 +10,8 @@
   title        = {{10 CFR Part 50.34}},
   author       = {{U.S. Nuclear Regulatory Commission}},
   howpublished = {Code of Federal Regulations},
-  urldate     = {2025-12-05},
+  urlyear = {2025},
+	month = dec,
   url          = {https://www.nrc.gov/reading-rm/doc-collections/cfr/part050/part050-0034}
 }
 
@@ -18,50 +19,54 @@
   title = {{10 CFR Part 55.59}},
   author       = {{U.S. Nuclear Regulatory Commission}},
   howpublished = {Code of Federal Regulations},
-  urldate     = {2025-12-05},
+  urlyear = {2025},
+	month = dec,
   url          = {https://www.nrc.gov/reading-rm/doc-collections/cfr/part055/part055-0059}
 }
 
-@techreport{WRPS.Description,
-    title = {{Westinghouse RPS System Description}},
-    institution = {Westinghouse Electric Corporation},
-    url = {https://nrcoe.inl.gov/publicdocs/SystemStudies/rps-w-description.pdf},
-    urldate = {2025-12-05}
-}
-
-@online{gentillon_westinghouse_1999,
-	title = {Westinghouse Reactor Protection System Unavailability, 1984-1995},
-	url = {https://digital.library.unt.edu/ark:/67531/metadc620476/},
-	titleaddon = {{PSA} '99, Washington, {DC} ({US}), 08/22/1999--08/25/1999},
-	type = {Article},
-	author = {Gentillon, C. D. and Marksberry, D. and Rasmuson, D. and Calley, M. B. and Eide, S. A. and Wierman, T.},
-	urldate = {2025-12-05},
-	date = {1999-08-01},
-	note = {Number: {INEEL}/{CON}-99-00374
-Publisher: Idaho National Engineering and Environmental Laboratory},
-	file = {Full Text PDF:/home/danesabo/Zotero/storage/7QKWQ8NI/Gentillon et al. - 1999 - Westinghouse Reactor Protection System Unavailability, 1984-1995.pdf:application/pdf},
-}
-
-@online{operator_statistics,
-	title = {{Operator Licensing}},
-  author       = {{U.S. Nuclear Regulatory Commission}},
-  howpublished = {\url{https://www.nrc.gov/reactors/operator-licensing}},
-	urldate = {2025-11-28},
-	file = {Operator Licensing | Nuclear Regulatory Commission:/home/danesabo/Zotero/storage/KUP9B5GH/operator-licensing.html:text/html},
-}
-
 @misc{10CFR55,
 	title = {{Part 55—Operators' Licenses}},
 	author = {{U.S. Nuclear Regulatory Commission}},
 	howpublished = {\url{https://www.nrc.gov/reading-rm/doc-collections/cfr/part055/full-text}},
 }
 
-@online{10CFR50.54,
+@misc{10CFR50.54,
 	title = {{§ 50.54 Conditions of Licenses}},
   author = {{U.S. Nuclear Regulatory Commission}},
 	howpublished = {\url{https://www.nrc.gov/reading-rm/doc-collections/cfr/part050/part050-0054}},
-	urldate = {2025-11-28},
-	file = {§ 50.54 Conditions of licenses. | Nuclear Regulatory Commission:/home/danesabo/Zotero/storage/THTZUD3T/part050-0054.html:text/html},
+	urlyear = {2025},
+	month = nov,
+}
+
+@techreport{WRPS.Description,
+    author = {{Westinghouse Electric Corporation}},
+    title = {{Westinghouse RPS System Description}},
+    institution = {Westinghouse Electric Corporation},
+    url = {https://nrcoe.inl.gov/publicdocs/SystemStudies/rps-w-description.pdf},
+    urlyear = {2025},
+	month = dec
+}
+
+@misc{gentillon_westinghouse_1999,
+	title = {Westinghouse Reactor Protection System Unavailability, 1984-1995},
+	url = {https://digital.library.unt.edu/ark:/67531/metadc620476/},
+	note = {{PSA} '99, Washington, {DC} ({US}), 08/22/1999--08/25/1999},
+	type = {Article},
+	author = {Gentillon, C. D. and Marksberry, D. and Rasmuson, D. and Calley, M. B. and Eide, S. A. and Wierman, T.},
+	urlyear = {2025},
+	month = dec,
+	year = {1999},
+	month = aug,
+	note = {Number: {INEEL}/{CON}-99-00374
+Publisher: Idaho National Engineering and Environmental Laboratory},
+}
+
+@misc{operator_statistics,
+	title = {{Operator Licensing}},
+  author       = {{U.S. Nuclear Regulatory Commission}},
+  howpublished = {\url{https://www.nrc.gov/reactors/operator-licensing}},
+	urlyear = {2025},
+	month = nov,
 }
 
 @techreport{Kemeny1979,
@@ -72,6 +77,12 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
   month       = {October}
 }
 
+@article{noauthor_human_nodate,
+	title = {Human {Performance} {Improvement} {Handbook}, {Volume} 1},
+	language = {en},
+	file = {PDF:/Users/danesabo/Zotero/storage/HQZTH3YI/Human Performance Improvement Handbook, Volume 1.pdf:application/pdf},
+}
+
 @misc{WNA2020,
   title        = {Safety of Nuclear Power Reactors},
   author       = {{World Nuclear Association}},
@@ -87,14 +98,14 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	doi = {10.1007/s13280-013-0382-x},
 	pages = {267--284},
 	number = {3},
-	journaltitle = {Ambio},
-	shortjournal = {Ambio},
+	journal = {Ambio},
 	author = {Högberg, Lars},
-	urldate = {2025-12-05},
-	date = {2013-04},
+	urlyear = {2025},
+	month = dec,
+	year = {2013},
+	month = apr,
 	pmid = {23423737},
 	pmcid = {PMC3606704},
-	file = {Full Text:/home/danesabo/Zotero/storage/E8F2QZGR/Högberg - 2013 - Root Causes and Impacts of Severe Accidents at Large Nuclear Power Plants.pdf:application/pdf},
 }
 
 @article{zhang_analysis_2025,
@@ -105,13 +116,13 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	doi = {10.1016/j.net.2025.103687},
 	pages = {103687},
 	number = {10},
-	journaltitle = {Nuclear Engineering and Technology},
-	shortjournal = {Nuclear Engineering and Technology},
+	journal = {Nuclear Engineering and Technology},
 	author = {Zhang, Meihui and Dai, Licao and Chen, Wenming and Pang, Ensheng},
-	urldate = {2025-12-05},
-	date = {2025-10-01},
+	urlyear = {2025},
+	month = dec,
+	year = {2025},
+	month = oct,
 	keywords = {Active errors, {HFACS} model, Latent errors, Licensee event reports},
-	file = {ScienceDirect Snapshot:/home/danesabo/Zotero/storage/N5R2Z3GL/S1738573325002554.html:text/html},
 }
 
 @techreport{Kiniry2024,
@@ -144,19 +155,92 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 }
 
 @book{baier_principles_2008,
-	location = {Cambridge, {MA}, {USA}},
+	address = {Cambridge, {MA}, {USA}},
 	title = {Principles of Model Checking},
 	isbn = {978-0-262-02649-9},
 	abstract = {A comprehensive introduction to the foundations of model checking, a fully automated technique for finding flaws in hardware and software; with extensive examples and both practical and theoretical exercises.},
-	pagetotal = {984},
 	publisher = {{MIT} Press},
 	author = {Baier, Christel and Katoen, Joost-Pieter},
-	date = {2008-04-25},
-	langid = {english},
+	year = {2008},
+	month = apr,
+}
+
+@article{platzer_differential_2008,
+	title = {Differential {Dynamic} {Logic} for {Hybrid} {Systems}},
+	volume = {41},
+	issn = {1573-0670},
+	url = {https://doi.org/10.1007/s10817-008-9103-8},
+	doi = {10.1007/s10817-008-9103-8},
+	abstract = {Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce a dynamic logic for hybrid programs, which is a program notation for hybrid systems. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid programs to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. In a case study with cooperating traffic agents of the European Train Control System, we further show that our calculus is well-suited for verifying realistic hybrid systems with parametric system dynamics.},
+	language = {en},
+	number = {2},
+	urlyear = {2025},
+	month = sep,
+	journal = {Journal of Automated Reasoning},
+	author = {Platzer, André},
+	month = aug,
+	year = {2008},
+	keywords = {Automated theorem proving, Axiomatisation, Differential equations, Dynamic logic, Sequent calculus, Verification of hybrid systems},
+	pages = {143--189},
+}
+
+@inproceedings{fulton_keymaera_2015,
+	address = {Cham},
+	title = {{KeYmaera} {X}: {An} {Axiomatic} {Tactical} {Theorem} {Prover} for {Hybrid} {Systems}},
+	isbn = {978-3-319-21401-6},
+	shorttitle = {{KeYmaera} {X}},
+	doi = {10.1007/978-3-319-21401-6_36},
+	abstract = {KeYmaera X is a theorem prover for differential dynamic logic (), a logic for specifying and verifying properties of hybrid systems. Reasoning about complicated hybrid systems models requires support for sophisticated proof techniques, efficient computation, and a user interface that crystallizes salient properties of the system. KeYmaera X allows users to specify custom proof search techniques as tactics, execute these tactics in parallel, and interface with partial proofs via an extensible user interface.},
+	language = {en},
+	booktitle = {Automated {Deduction} - {CADE}-25},
+	publisher = {Springer International Publishing},
+	author = {Fulton, Nathan and Mitsch, Stefan and Quesel, Jan-David and Völp, Marcus and Platzer, André},
+	editor = {Felty, Amy P. and Middeldorp, Aart},
+	year = {2015},
+	keywords = {Adaptive Cruise Control, Hybrid automaton, Proof Rule, Proof Tree, Sequent calculus},
+	pages = {527--538},
+}
+
+@inproceedings{alur_hybrid_1993,
+	address = {Berlin, Heidelberg},
+	title = {Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems},
+	isbn = {978-3-540-48060-0},
+	doi = {10.1007/3-540-57318-6_30},
+	shorttitle = {Hybrid automata},
+	pages = {209--229},
+	booktitle = {Hybrid Systems},
+	publisher = {Springer},
+	author = {Alur, Rajeev and Courcoubetis, Costas and Henzinger, Thomas A. and Ho, Pei -Hsin},
+	editor = {Grossman, Robert L. and Nerode, Anil and Ravn, Anders P. and Rischel, Hans},
+	year = {1993},
+	keywords = {Acceptance Condition, Hybrid Automaton, Hybrid System, Mutual Exclusion, Reachability Problem},
+}
+
+@techreport{katis_realizability_2022,
+	title = {Realizability {Checking} of {Requirements} in {FRET}},
+	url = {https://ntrs.nasa.gov/citations/20220007510},
+	abstract = {Requirements formalization has become increasingly popular in industrial settings as an
+effort to disambiguate designs and optimize development time and costs for critical system components. Formal requirements elicitation also enables the employment of analysis
+tools to prove important properties, such as consistency and realizability. In this report,
+we present the realizability analysis framework that we developed as part of the Formal
+Requirements Elicitation Tool (FRET). Our framework prioritizes usability, and employs
+state-of-the-art analysis algorithms that support infinite theories. We demonstrate the workflow for realizability checking, showcase the diagnosis process that supports visualization of
+conflicts between requirements and simulation of counterexamples, and discuss results from
+industrial-level case studies.},
+	urlyear = {2026},
+	month = mar,
+	institution = {NASA Ames Research Center},
+	author = {Katis, Andreas and Mavridou, Anastasia and Giannakopoulou, Dimitra and Pressburger, Thomas and Schumann, Johann},
+	month = apr,
+	year = {2022},
+	note = {NTRS Author Affiliations: Wyle (United States), Ames Research Center
+NTRS Document ID: 20220007510
+NTRS Research Center: Ames Research Center (ARC)},
+	keywords = {Mathematical And Computer Sciences (General)},
 }
 
 @inproceedings{katis_capture_2022,
-	location = {Cham},
+	address = {Cham},
 	title = {Capture, Analyze, Diagnose: Realizability Checking Of Requirements in {FRET}},
 	isbn = {978-3-031-13188-2},
 	doi = {10.1007/978-3-031-13188-2_24},
@@ -166,13 +250,27 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	publisher = {Springer International Publishing},
 	author = {Katis, Andreas and Mavridou, Anastasia and Giannakopoulou, Dimitra and Pressburger, Thomas and Schumann, Johann},
 	editor = {Shoham, Sharon and Vizel, Yakir},
-	date = {2022},
-	langid = {english},
-	file = {Full Text PDF:/home/danesabo/Zotero/storage/3JPVH8U2/Katis et al. - 2022 - Capture, Analyze, Diagnose Realizability Checking Of Requirements in FRET.pdf:application/pdf},
+	year = {2022},
+}
+
+@techreport{pressburger_using_2023,
+	title = {Using {FRET} to {Create}, {Analyze} and {Monitor} {Requirements} for a {Lift} {Plus} {Cruise} {Case} {Study}},
+	url = {https://ntrs.nasa.gov/citations/20220017032},
+	abstract = {In this technical report we provide information on the use of the NASA Formal RequirementsElicitation Tool (FRET) to create requirements for a Lift Plus Cruise (LPC) aircraft case study.  Furthermore, we provide details on using FRET to translate these requirements into an appropriate format for the Copilot tool, enabling their usage to perform runtime verification on a synthesized LPC system.},
+	urlyear = {2026},
+	month = mar,
+	institution = {NASA Ames Research Center},
+	author = {Pressburger, Thomas and Katis, Andreas and Dutle, Aaron and Mavridou, Anastasia},
+	month = apr,
+	year = {2023},
+	note = {NTRS Author Affiliations: Ames Research Center, KBR (United States), Langley Research Center
+NTRS Document ID: 20220017032
+NTRS Research Center: Ames Research Center (ARC)},
+	keywords = {Mathematical And Computer Sciences (General)},
 }
 
 @inproceedings{meyer_strix_2018,
-	location = {Cham},
+	address = {Cham},
 	title = {Strix: Explicit Reactive Synthesis Strikes Back!},
 	isbn = {978-3-319-96145-3},
 	doi = {10.1007/978-3-319-96145-3_31},
@@ -182,8 +280,7 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	publisher = {Springer International Publishing},
 	author = {Meyer, Philipp J. and Sickert, Salomon and Luttenberger, Michael},
 	editor = {Chockler, Hana and Weissenbacher, Georg},
-	date = {2018},
-	langid = {english},
+	year = {2018},
 }
 
 @misc{jacobs_reactive_2024,
@@ -194,12 +291,26 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	number = {{arXiv}:2206.00251},
 	publisher = {{arXiv}},
 	author = {Jacobs, Swen and others},
-	urldate = {2025-12-06},
-	date = {2024-05-06},
-	eprinttype = {arxiv},
-	eprint = {2206.00251 [cs]},
+	urlyear = {2025},
+	month = dec,
+	year = {2024},
+	month = may,
 	keywords = {Computer Science - Logic in Computer Science},
-	file = {Preprint PDF:/home/danesabo/Zotero/storage/GU6W5UH4/Jacobs et al. - 2024 - The Reactive Synthesis Competition (SYNTCOMP) 2018-2021.pdf:application/pdf;Snapshot:/home/danesabo/Zotero/storage/57UPK6A5/2206.html:text/html},
+}
+
+@book{lunze_handbook_2009,
+	address = {Cambridge},
+	title = {Handbook of {Hybrid} {Systems} {Control}: {Theory}, {Tools}, {Applications}},
+	isbn = {978-0-521-76505-3},
+	shorttitle = {Handbook of {Hybrid} {Systems} {Control}},
+	url = {https://www.cambridge.org/core/books/handbook-of-hybrid-systems-control/95CBB51B339FA6B95B814D4BABB715A7},
+	doi = {10.1017/CBO9780511807930},
+	abstract = {Setting out core theory and reviewing a range of new methods, theoretical problems and applications, this handbook shows how hybrid dynamical systems can be modelled and understood. Sixty expert authors involved in the recent research activities and industrial application studies provide practical insights on topics ranging from the theoretical investigations over computer-aided design to applications in energy management and the process industry. Structured into three parts, the book opens with a thorough introduction to hybrid systems theory, illustrating new dynamical phenomena through numerous examples. Part II then provides a survey of key tools and tool integration activities. Finally, Part III is dedicated to applications, implementation issues and system integration, considering different domains such as industrial control, automotive systems and digital networks. Three running examples are referred to throughout the book, together with numerous illustrations, helping both researchers and industry professionals to understand complex theory, recognise problems and find appropriate solutions.},
+	urlyear = {2026},
+	month = jan,
+	publisher = {Cambridge University Press},
+	editor = {Lunze, Jan and Lamnabhi-Lagarrigue, Françoise},
+	year = {2009},
 }
 
 @article{branicky_multiple_1998,
@@ -210,41 +321,74 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	doi = {10.1109/9.664150},
 	pages = {475--482},
 	number = {4},
-	journaltitle = {{IEEE} Transactions on Automatic Control},
+	journal = {{IEEE} Transactions on Automatic Control},
 	author = {Branicky, M.S.},
-	urldate = {2025-09-10},
-	date = {1998-04},
+	urlyear = {2025},
+	month = sep,
+	year = {1998},
+	month = apr,
 	keywords = {Automata, Control systems, Difference equations, Differential equations, Lagrangian functions, Limit-cycles, Lyapunov method, Stability analysis, Switched systems, Switches},
-	file = {PDF:/home/danesabo/Zotero/storage/5AQWDPAA/Branicky - 1998 - Multiple Lyapunov functions and other analysis tools for switched and hybrid systems.pdf:application/pdf},
 }
 
-@thesis{guernic_reachability_2009,
+@phdthesis{kapuria_using_2025,
+	address = {United States -- Pennsylvania},
+	type = {Ph.{D}.},
+	title = {Using {Decomposition}-{Based} {Formal} {Verification} to {Analyze} {Safety} and {Identify} {Unsafe} {Control} {Actions} for {Hybrid} {Systems}},
+	copyright = {Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.},
+	isbn = {9798280700147},
+	url = {https://www.proquest.com/docview/3215670525/abstract/3C715CB23CB84313PQ/1},
+	abstract = {This dissertation presents a decomposition-based formal verification framework for hybrid systems, focusing on identifying unsafe control actions (UCAs) in cyber-physical systems (CPS). Using differential dynamic logic, we verify safety properties by first proving correctness at the component level before integrating them into a system-wide proof. Our approach enhances scalability by isolating subsystems, enforcing constraints on their interactions, and using satisfiability modulo theories (SMT) solvers to automate invariant generation. We apply this methodology to a small modular advanced high-temperature reactor (SmAHTR), analyzing its control logic under both normal operations and adversarial conditions, including cyberattacks. The results demonstrate how formal methods can systematically identify UCAs that emerge from mode transitions, feedback interactions, and incorrect assumptions. By integrating theorem proving with reachability analysis, this work advances CPS safety verification, providing a rigorous and scalable approach to ensuring system resilience.
+To achieve this, we develop a hybrid automaton model of SmAHTR and formally verify its behavior under various control strategies, including scenarios involving maintenance operations and external disruptions. We introduce a structured method to decompose the system into independently analyzable components, ensuring that local safety guarantees extend to global system correctness. The verification process captures both intended and unintended control actions, revealing potential failure modes that traditional analysis methods might overlook. Furthermore, we propose an automated approach for identifying UCAs by leveraging formal reasoning tools to systematically explore system behaviors beyond manual hazard analysis. Our findings demonstrate that decomposition-based verification not only reduces computational complexity but also improves the efficiency and robustness of CPS safety analysis, particularly for high-assurance applications such as nuclear reactor operations.},
+	language = {English},
+	urlyear = {2026},
+	month = feb,
+	school = {University of Pittsburgh},
+	author = {Kapuria, Abhimanyu},
+	year = {2025},
+	keywords = {Computer science, Differential equations, Electrical engineering, Engineering, Formal verification, Hybrid systems, Mechanical engineering, Reachability analysis, Satisfiability modulo theories solvers},
+}
+
+@inproceedings{lang_formal_2021,
+	address = {VIRTUAL EVENT},
+	title = {Formal {Verification} {Applied} to {Spacecraft} {Attitude} {Control}},
+	isbn = {978-1-62410-609-5},
+	url = {https://arc.aiaa.org/doi/10.2514/6.2021-1126},
+	doi = {10.2514/6.2021-1126},
+	language = {en},
+	urlyear = {2024},
+	month = nov,
+	booktitle = {{AIAA} {Scitech} 2021 {Forum}},
+	publisher = {American Institute of Aeronautics and Astronautics},
+	author = {Lang, Kendra and Klett, Corbin and Hawkins, Kelsey and Feron, Eric and Tsiotras, Panagiotis and Phillips, Sean},
+	month = jan,
+	year = {2021},
+}
+
+@inproceedings{frehse_spaceex_2011,
+	address = {Berlin, Heidelberg},
+	title = {{SpaceEx}: Scalable Verification of Hybrid Systems},
+	isbn = {978-3-642-22110-1},
+	doi = {10.1007/978-3-642-22110-1_30},
+	shorttitle = {{SpaceEx}},
+	pages = {379--395},
+	booktitle = {Computer Aided Verification},
+	publisher = {Springer},
+	author = {Frehse, Goran and Le Guernic, Colas and Donzé, Alexandre and Cotton, Scott and Ray, Rajarshi and Lebeltel, Olivier and Ripado, Rodolfo and Girard, Antoine and Dang, Thao and Maler, Oded},
+	editor = {Gopalakrishnan, Ganesh and Qadeer, Shaz},
+	year = {2011},
+	keywords = {Hybrid Automaton, Hybrid System, Reachability Analysis, Reachable State, Support Function},
+}
+
+@phdthesis{guernic_reachability_2009,
 	title = {Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics},
 	url = {https://theses.hal.science/tel-00422569},
 	institution = {Université Joseph-Fourier - Grenoble I},
-	type = {phdthesis},
+	school = {Université Joseph-Fourier, Grenoble},
 	author = {Guernic, Colas Le},
-	urldate = {2025-09-14},
-	date = {2009-10-28},
-	langid = {english},
-	file = {Full Text PDF:/home/danesabo/Zotero/storage/A5XNTDZ9/Guernic - 2009 - Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics.pdf:application/pdf},
-}
-
-@inproceedings{alur_hybrid_1993,
-	location = {Berlin, Heidelberg},
-	title = {Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems},
-	isbn = {978-3-540-48060-0},
-	doi = {10.1007/3-540-57318-6_30},
-	shorttitle = {Hybrid automata},
-	pages = {209--229},
-	booktitle = {Hybrid Systems},
-	publisher = {Springer},
-	author = {Alur, Rajeev and Courcoubetis, Costas and Henzinger, Thomas A. and Ho, Pei -Hsin},
-	editor = {Grossman, Robert L. and Nerode, Anil and Ravn, Anders P. and Rischel, Hans},
-	date = {1993},
-	langid = {english},
-	keywords = {Acceptance Condition, Hybrid Automaton, Hybrid System, Mutual Exclusion, Reachability Problem},
-	file = {Full Text PDF:/home/danesabo/Zotero/storage/WBXYUC86/Alur et al. - 1993 - Hybrid automata An algorithmic approach to the specification and verification of hybrid systems.pdf:application/pdf},
+	urlyear = {2025},
+	month = sep,
+	year = {2009},
+	month = oct,
 }
 
 @article{mitchell_time-dependent_2005,
@@ -255,29 +399,13 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	doi = {10.1109/TAC.2005.851439},
 	pages = {947--957},
 	number = {7},
-	journaltitle = {{IEEE} Transactions on Automatic Control},
+	journal = {{IEEE} Transactions on Automatic Control},
 	author = {Mitchell, I.M. and Bayen, A.M. and Tomlin, C.J.},
-	urldate = {2025-09-15},
-	date = {2005-07},
+	urlyear = {2025},
+	month = sep,
+	year = {2005},
+	month = jul,
 	keywords = {Aircraft, Collaborative software, Collision avoidance, Computational modeling, Differential games, Hamilton–Jacobi equations, Nonlinear equations, Nonlinear systems, Partial differential equations, reachability, Trajectory, Vehicle dynamics, verification, Viscosity},
-	file = {Snapshot:/home/danesabo/Zotero/storage/SLKV9PEI/1463302.html:text/html;Submitted Version:/home/danesabo/Zotero/storage/9YWL2UDH/Mitchell et al. - 2005 - A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games.pdf:application/pdf},
-}
-
-@inproceedings{frehse_spaceex_2011,
-	location = {Berlin, Heidelberg},
-	title = {{SpaceEx}: Scalable Verification of Hybrid Systems},
-	isbn = {978-3-642-22110-1},
-	doi = {10.1007/978-3-642-22110-1_30},
-	shorttitle = {{SpaceEx}},
-	pages = {379--395},
-	booktitle = {Computer Aided Verification},
-	publisher = {Springer},
-	author = {Frehse, Goran and Le Guernic, Colas and Donzé, Alexandre and Cotton, Scott and Ray, Rajarshi and Lebeltel, Olivier and Ripado, Rodolfo and Girard, Antoine and Dang, Thao and Maler, Oded},
-	editor = {Gopalakrishnan, Ganesh and Qadeer, Shaz},
-	date = {2011},
-	langid = {english},
-	keywords = {Hybrid Automaton, Hybrid System, Reachability Analysis, Reachable State, Support Function},
-	file = {Full Text PDF:/home/danesabo/Zotero/storage/LPQK8GY2/Frehse et al. - 2011 - SpaceEx Scalable Verification of Hybrid Systems.pdf:application/pdf},
 }
 
 @inproceedings{bansal_hamilton-jacobi_2017,
@@ -289,14 +417,15 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	pages = {2242--2253},
 	booktitle = {2017 {IEEE} 56th Annual Conference on Decision and Control ({CDC})},
 	author = {Bansal, Somil and Chen, Mo and Herbert, Sylvia and Tomlin, Claire J.},
-	urldate = {2025-09-15},
-	date = {2017-12},
+	urlyear = {2025},
+	month = sep,
+	year = {2017},
+	month = dec,
 	keywords = {Aircraft, Games, Level set, Safety, Tools, Trajectory, Tutorials},
-	file = {Snapshot:/home/danesabo/Zotero/storage/EEK5IE93/8263977.html:text/html;Submitted Version:/home/danesabo/Zotero/storage/BMNLZ9DW/Bansal et al. - 2017 - Hamilton-Jacobi reachability A brief overview and recent advances.pdf:application/pdf},
 }
 
 @inproceedings{prajna_safety_2004,
-	location = {Berlin, Heidelberg},
+	address = {Berlin, Heidelberg},
 	title = {Safety Verification of Hybrid Systems Using Barrier Certificates},
 	isbn = {978-3-540-24743-2},
 	doi = {10.1007/978-3-540-24743-2_32},
@@ -305,7 +434,111 @@ Publisher: Idaho National Engineering and Environmental Laboratory},
 	publisher = {Springer},
 	author = {Prajna, Stephen and Jadbabaie, Ali},
 	editor = {Alur, Rajeev and Pappas, George J.},
-	date = {2004},
-	langid = {english},
+	year = {2004},
 	keywords = {Continuous State, Discrete Transition, Hybrid System, Integral Constraint, Reachability Analysis},
 }
+
+@techreport{deroucy_ai_2025,
+  title       = {AI, Data Centers and Energy Demand: Reassessing and Exploring the Trends},
+  author      = {de Roucy-Rochegonde, Laure and Buffard, Adrien},
+  institution = {French Institute of International Relations (Ifri)},
+  year        = {2025},
+  type        = {Ifri Papers},
+  isbn        = {979-10-373-1000-2}
+}
+
+
+@article{harvey_levels_2021,
+	title = {The {Levels} of {War} as {Levels} of {Analysis}},
+	language = {en},
+	publisher = {Military Review},
+	author = {Harvey, Andrew S},
+	year = {2021},
+	file = {PDF:/Users/danesabo/Zotero/storage/5NSKMNEU/Harvey - The Levels of War as Levels of Analysis.pdf:application/pdf},
+}
+
+@article{luttenberger_practical_2020,
+	title = {Practical synthesis of reactive systems from {LTL} specifications via parity games},
+	volume = {57},
+	issn = {1432-0525},
+	url = {https://doi.org/10.1007/s00236-019-00349-3},
+	doi = {10.1007/s00236-019-00349-3},
+	abstract = {The synthesis of reactive systems from linear temporal logic (LTL) specifications is an important aspect in the design of reliable software and hardware. We present our adaption of the classic automata-theoretic approach to LTL synthesis, implemented in the tool Strix which has won the two last synthesis competitions (Syntcomp2018/2019). The presented approach is (1) structured, meaning that the states used in the construction have a semantic structure that is exploited in several ways, it performs a (2) forward exploration such that it often constructs only a small subset of the reachable states, and it is (3) incremental in the sense that it reuses results from previous inconclusive solution attempts. Further, we present and study different guiding heuristics that determine where to expand the on-demand constructed arena. Moreover, we show several techniques for extracting an implementation (Mealy machine or circuit) from the witness of the tree-automaton emptiness check. Lastly, the chosen constructions use a symbolic representation of the transition functions to reduce runtime and memory consumption. We evaluate the proposed techniques on the Syntcomp2019 benchmark set and show in more detail how the proposed techniques compare to the techniques implemented in other leading LTL synthesis tools.},
+	language = {en},
+	number = {1},
+	urldate = {2026-03-07},
+	journal = {Acta Informatica},
+	author = {Luttenberger, Michael and Meyer, Philipp J. and Sickert, Salomon},
+	month = apr,
+	year = {2020},
+	pages = {3--36},
+	file = {Submitted Version:/Users/danesabo/Zotero/storage/VYMVF5GK/Luttenberger et al. - 2020 - Practical synthesis of reactive systems from LTL specifications via parity games.pdf:application/pdf},
+}
+
+
+@inproceedings{chen_taylor_2012,
+	title = {Taylor {Model} {Flowpipe} {Construction} for {Non}-linear {Hybrid} {Systems}},
+	issn = {1052-8725},
+	url = {https://ieeexplore.ieee.org/document/6424802},
+	doi = {10.1109/RTSS.2012.70},
+	abstract = {We propose an approach for verifying non-linear hybrid systems using higher-order Taylor models that are a combination of bounded degree polynomials over the initial conditions and time, bloated by an interval. Taylor models are an effective means for computing rigorous bounds on the complex time trajectories of non-linear differential equations. As a result, Taylor models have been successfully used to verify properties of non-linear continuous systems. However, the handling of discrete (controller) transitions remains a challenging problem. In this paper, we provide techniques for handling the effect of discrete transitions on Taylor model flow pipe construction. We explore various solutions based on two ideas: domain contraction and range over-approximation. Instead of explicitly computing the intersection of a Taylor model with a guard set, domain contraction makes the domain of a Taylor model smaller by cutting away parts for which the intersection is empty. It is complemented by range over-approximation that translates Taylor models into commonly used representations such as template polyhedra or zonotopes, on which intersections with guard sets have been previously studied. We provide an implementation of the techniques described in the paper and evaluate the various design choices over a set of challenging benchmarks.},
+	urldate = {2026-03-18},
+	booktitle = {2012 {IEEE} 33rd {Real}-{Time} {Systems} {Symposium}},
+	author = {Chen, Xin and Ábrahám, Erika and Sankaranarayanan, Sriram},
+	month = dec,
+	year = {2012},
+	note = {ISSN: 1052-8725},
+	keywords = {Approximation methods, Computational modeling, Mathematical model, Polynomials, Safety, Taylor series, Trajectory},
+	pages = {183--192},
+	file = {Snapshot:/Users/danesabo/Zotero/storage/7HBF3VMT/6424802.html:text/html},
+}
+
+@inproceedings{chen_flow_2013,
+	address = {Berlin, Heidelberg},
+	title = {Flow*: {An} {Analyzer} for {Non}-linear {Hybrid} {Systems}},
+	isbn = {978-3-642-39799-8},
+	shorttitle = {Flow*},
+	doi = {10.1007/978-3-642-39799-8_18},
+	abstract = {The tool Flow* performs Taylor model-based flowpipe construction for non-linear (polynomial) hybrid systems. Flow* combines well-known Taylor model arithmetic techniques for guaranteed approximations of the continuous dynamics in each mode with a combination of approaches for handling mode invariants and discrete transitions. Flow* supports a wide variety of optimizations including adaptive step sizes, adaptive selection of approximation orders and the heuristic selection of template directions for aggregating flowpipes. This paper describes Flow* and demonstrates its performance on a series of non-linear continuous and hybrid system benchmarks. Our comparisons show that Flow* is competitive with other tools.},
+	language = {en},
+	booktitle = {Computer {Aided} {Verification}},
+	publisher = {Springer},
+	author = {Chen, Xin and Ábrahám, Erika and Sankaranarayanan, Sriram},
+	editor = {Sharygina, Natasha and Veith, Helmut},
+	year = {2013},
+	keywords = {Adaptive Step, Adaptive Step Size, Discrete Transition, Hybrid System, Taylor Model},
+	pages = {258--263},
+	file = {Full Text PDF:/Users/danesabo/Zotero/storage/6QV2XCVF/Chen et al. - 2013 - Flow An Analyzer for Non-linear Hybrid Systems.pdf:application/pdf},
+}
+
+
+@inproceedings{althoff_introduction_nodate,
+	title = {An {Introduction} to {CORA} 2015},
+	url = {https://easychair.org/publications/paper/xMm},
+	doi = {10.29007/zbkv},
+	abstract = {The philosophy, architecture, and capabilities of the COntinuous Reachability Analyzer (CORA) are presented. CORA is a toolbox that integrates various vector and matrix set representations and operations on them as well as reachability algorithms of various dynamic system classes. The software is designed such that set representations can be exchanged without having to modify the code for reachability analysis. CORA has a modular design, making it possible to use the capabilities of the various set representations for other purposes besides reachability analysis. The toolbox is designed using the object oriented paradigm, such that users can safely use methods without concerning themselves with detailed information hidden inside the object. Since the toolbox is written in MATLAB, the installation and use is platform independent.},
+	urldate = {2026-03-18},
+	author = {Althoff, Matthias},
+	pages = {120--87},
+	file = {Full Text:/Users/danesabo/Zotero/storage/BIGJMRCV/Althoff - An Introduction to CORA 2015.pdf:application/pdf},
+}
+
+
+@article{bogomolov_reachability_2020,
+	title = {Reachability {Analysis} of {Linear} {Hybrid} {Systems} via {Block} {Decomposition}},
+	volume = {39},
+	issn = {1937-4151},
+	url = {https://ieeexplore.ieee.org/document/9211556},
+	doi = {10.1109/TCAD.2020.3012859},
+	abstract = {Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this article, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.},
+	number = {11},
+	urldate = {2026-03-18},
+	journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems},
+	author = {Bogomolov, Sergiy and Forets, Marcelo and Frehse, Goran and Potomkin, Kostiantyn and Schilling, Christian},
+	month = nov,
+	year = {2020},
+	keywords = {Approximation algorithms, Decomposition, Design automation, Heuristic algorithms, hybrid systems, Integrated circuits, Linear systems, reachability, Reachability analysis, Tools},
+	pages = {4018--4029},
+	file = {Snapshot:/Users/danesabo/Zotero/storage/D7FYXW7T/9211556.html:text/html;Submitted Version:/Users/danesabo/Zotero/storage/I3HNBQ65/Bogomolov et al. - 2020 - Reachability Analysis of Linear Hybrid Systems via Block Decomposition.pdf:application/pdf},
+}
+