% Approach Overview
\begin{frame}{Unifying discrete synthesis and continuous verification enables end-to-end guarantees}

  \begin{center}
    \begin{tikzpicture}[node distance=1.5cm, auto, scale=0.85, transform shape]
      \tikzstyle{box} = [rectangle, rounded corners, minimum width=3.5cm, minimum height=1.2cm, text centered, draw=black, fill=blue!20, font=\small]
      \tikzstyle{arrow} = [->, >=stealth, very thick]
      \tikzstyle{tool} = [font=\tiny, text=green!50!black]

      % Thrust 1
      \node[box] (proc) {Procedures};
      \node[box, right=of proc] (ltl) {Temporal\\Logic};
      \draw[arrow] (proc) -- node[above] {\textbf{Thrust 1}} (ltl);
      \node[tool, below=0.1cm of ltl] {FRET};

      % Thrust 2
      \node[box, right=of ltl] (auto) {Discrete\\Automaton};
      \draw[arrow] (ltl) -- node[above] {\textbf{Thrust 2}} (auto);
      \node[tool, below=0.1cm of auto] {Synthesis};

      % Thrust 3
      \node[box, right=of auto] (cont) {Continuous\\Modes};
      \draw[arrow] (auto) -- node[above] {\textbf{Thrust 3}} (cont);
      \node[tool, below=0.1cm of cont] {Reachability};
    \end{tikzpicture}
  \end{center}

  \vspace{0.5cm}

  \begin{center}
    \begin{tikzpicture}
      \draw[thick, fill=gray!20] (0,0) rectangle (12,3);
      \node[align=center, text width=10cm] at (6,1.5) {
        \textbf{FIGURE: Detailed Pipeline Diagram}\\[0.2cm]
        Show example flowing through all three thrusts\\
        with visual representations of transformations
      };
    \end{tikzpicture}
  \end{center}

  %SPEAKER NOTES: See comments below
%
    \textbf{Three-Thrust Integrated Approach:}

    \textbf{Thrust 1 (Procedures → Temporal Logic):}
    Use NASA FRET to translate written procedures to formal specifications.
    Example: ``If high temp, insert rods until reset'' becomes $G(T_{high} \rightarrow X(\text{rods} \wedge \ldots))$
    Realizability checking catches errors in procedures before implementation.

    \textbf{Thrust 2 (Temporal Logic → Discrete Automaton):}
    Reactive synthesis generates correct-by-construction state machine.
    Discrete controller is mathematically guaranteed to follow specifications.

    \textbf{Thrust 3 (Continuous Controllers):}
    Use reachability analysis and barrier certificates.
    Compositional verification: local proofs, global guarantees.

    \textbf{Innovation:} Each piece uses state-of-the-art tools; innovation is in the integration.
% (End of speaker notes)
\end{frame}