For the following considerations it is useful to have a finite automaton with output. For this we chose the finite transducer, which is defined as follows (cf. Yu (1997)[300]:P66f)(cf. figure 3.6):

with

- := Finite set of states
- := Set of initial states
- := Set of final states
- := Finite set of symbols forming the input alphabet
- := Finite set of symbols forming the output alphabet
- := Set of state and output transitions

Thus, a finite transducer is a generalization of a Mealy Automaton.

Gerd Doeben-Henisch 2010-03-03