---
tags: engineering, state, diagram, machines
author: Nguyen Xuan Anh
github_id: monotykamary
date: 2022-06-28
---
## What is a Moore machine?
A Moore machine is a [[Finite-state automata]] where the output values are determined by only its current state. Moore machines are a restricted type of a [[Finite-state transducer]].
![Moore Machine](_assets/Moore_Machine.jpg)
## Mathematical Model
As per the general classification noted on [UC Davis outline on transducers](https://www.cs.ucdavis.edu/~rogaway/classes/120/spring13/eric-transducers) (formatted with similar variables to [[Finite-state automata]]s), a deterministic Moore machine has 6 main variables associated with its definition (a sextuple): ($\Sigma$, $S$, $\Gamma$, $\delta$, $\omega$, $s_0$).
- $\Sigma$ is the _input alphabet_ (a finite non-empty set of symbols) -> our events;
- $S$ is a finite non-empty set of states;
- $\Gamma$ is the *output alphabet*;
- $\delta$ is the state-transition function: $\delta: S \times \Sigma \rightarrow S$
- $\omega$ is the output-transition function: $\omega: S \rightarrow \Gamma$
- $s_0$ is an _initial state_, an element of $S$; and
- $\delta \subseteq S \times (\Sigma \cup \{\epsilon\}) \times (\Gamma \cup \{\epsilon\}) \times S$ (where ε is the [empty string](https://en.wikipedia.org/wiki/Empty_string 'Empty string')) is the *transition relation*.
Given any initial state in $s_0$, to transition our state to the next state with our output alphabet, our transition would be:
$
\delta: s_0 \times \Sigma \rightarrow S
$
$
\omega: s_0 \rightarrow \Gamma
$
## Examples of basic Moore machines
Unlike a Mealy machine, we can't coalesce the transition and output functions together as a single transition function. The behavior of the output function is **synchronous** to the state change. As such, we end up with something like this (in Rescript):
```typescript
type trafficLightStatus =
| Red
| Amber
| Green
| FlashingRed
type input =
| ExpireTime
| Error
| Restart
type outputFn = (state) =>
switch (state) {
| Red => (Red, 60.0)
| Green => (Green, 60.0)
| Amber => (Amber, 60.0)
| FlashingRed => (FlashingRed, 30.0)
}
let transitionFn = (state, input) =>
switch (state, input) {
| (Red, ExpireTime) => Green(60.0)
| (Red, Error) => FlashingRed(30.0)
| (Green, ExpireTime) => Amber(60.0)
| (Green, Error) => FlashingRed(30.0)
| (Amber, ExpireTime) => Red(60.0)
| (Amber, Error) => FlashingRed(30.0)
| (FlashingRed, Restart) => Red(60.0)
| _ => state
};
let output = outputFn(transitionFn(Red, ExpireTime)) // (Green, 60.0)
```
## Differences between
### With formal [[Finite-state transducer]]s
Moore machines are a type of generator and are not used in processing natural language. As such, they do not have a concept of a final state.
### With [[Mealy Machine]]s
Both Mealy and Moore machines are generator-type state machines and can be used to parse [regular language](https://en.wikipedia.org/wiki/Regular_language). The outputs on a Mealy machine depend on **both the state and inputs**, whereas a Moore machine have their outputs **synchronously change with the state.**
> Every Moore machine can be converted to a Mealy machine and every Mealy machine can be converted to a Moore machine. Moore machine and Mealy machine are equivalent.
## Reference
- https://en.wikipedia.org/wiki/Mealy_machine
- https://www.cs.ucdavis.edu/~rogaway/classes/120/spring13/eric-transducers
- https://unstop.com/blog/difference-between-mealy-and-moore-machine