Editing Moore machine (section)

== Formal definition ==

A Moore machine can be defined as a [[N-tuple|6-tuple]] <math>(S, s_0, \Sigma, O, \delta, G)</math> consisting of the following:
* A finite set   of [[State (computer science)|states]] <math>S</math>
* A start state (also called initial state) <math>s_0</math> which is an element of <math>S</math>
* A finite set called the input [[Alphabet (computer science)|alphabet]] <math>\Sigma</math>
* A finite set called the output [[Alphabet (computer science)|alphabet]] <math>O</math>
* A transition [[function (mathematics)|function]] <math>\delta : S \times \Sigma \rightarrow S </math> mapping a state and the input alphabet to the next state
* An output function <math>G : S \rightarrow O</math> mapping each state to the output alphabet

"Evolution across time" is realized in this abstraction by having the state machine consult the time-changing input symbol at discrete "timer ticks" <math>t_0, t_1, t_2, ...</math> and react according to its internal configuration at those idealized instants, or else having the state machine wait for a next input symbol (as on a FIFO) and react whenever it arrives.

A Moore machine can be regarded as a restricted type of [[finite-state transducer]].