50 lines
1.3 KiB
Markdown
50 lines
1.3 KiB
Markdown
---
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id: 20251223165340
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title: Mealy Machines
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type: permanent
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created: 2025-12-23T21:53:40Z
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modified: 2025-12-23T22:38:18Z
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tags: []
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---
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# Mealy Machines
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Mealy machines are a formalization of a system that has
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states drawn as nodes and transitions drawn from state to
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state.
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From Wikipedia:
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```
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A mealy machine is a finite state machine whose
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output values are determined by both its current state, and
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the current inputs.
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```
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Mealy machines can also be defined as a six-tuple:
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$$(S, S_0, \Sigma, \Lambda, T, G)$$
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where
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- S is the finite set of states
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- S_0 is the start state
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- $\Sigma$ is the input alphabet
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- $\Lambda$ is the output alphabet
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- $T : S \times \Sigma \rightarrow S$ is the state
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transition function
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- $G : S \times \Sigma \rightarrow \Lambda$ is the output
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function
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Mealy machines have the advantage that they generally can
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produce smaller sized automata (aka less states). This is
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because transitions themselves in a Mealy machine are states
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in a Moore machine. The state of 'opening' in a Moore
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machine is the transition itself in a Mealy machine. Outputs
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aren't just based on state, so it isn't necesary to create a
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state to produce an output like a Moore machine. An output
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action can be created with the current state AND the input
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together.
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## Related
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[[Finite State Machines]]
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