---
id: 20251223165340
title: Mealy Machines
type: permanent
created: 2025-12-23T21:53:40Z
modified: 2025-12-23T22:38:18Z
tags: []
---

# Mealy Machines

Mealy machines are a formalization of a system that has
states drawn as nodes and transitions drawn from state to
state. 

From Wikipedia:
```
    A mealy machine is a finite state machine whose
output values are determined by both its current state, and
the current inputs.
```

Mealy machines can also be defined as a six-tuple:

$$(S, S_0, \Sigma, \Lambda, T, G)$$

where 
- S is the finite set of states
- S_0 is the start state
- $\Sigma$ is the input alphabet
- $\Lambda$ is the output alphabet
- $T : S \times \Sigma \rightarrow S$ is the state
transition function
- $G : S \times \Sigma \rightarrow \Lambda$ is the output
function

Mealy machines have the advantage that they generally can
produce smaller sized automata (aka less states). This is
because transitions themselves in a Mealy machine are states
in a Moore machine. The state of 'opening' in a Moore
machine is the transition itself in a Mealy machine. Outputs
aren't just based on state, so it isn't necesary to create a
state to produce an output like a Moore machine. An output
action can be created with the current state AND the input
together.

## Related
[[Finite State Machines]]