a finite set of states S {\displaystyle S} a start state (also called initial state) S 0 {\displaystyle S_{0}} which is an element of S {\displaystyle S} a finite set called the input alphabet Σ {\displaystyle \Sigma } a finite set called the output alphabet Λ {\displaystyle \Lambda } a transition function T : S × Σ → S {\displaystyle T:S\times \Sigma \rightarrow S} mapping pairs of a state and an input symbol to the corresponding next state. an output function G : S × Σ → Λ {\displaystyle G:S\times \Sigma \rightarrow \Lambda } mapping pairs of a state and an input symbol to the corresponding output symbol.