Automaton with Output

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):

$$\langle Q, I, F, \Sigma, \Xi, \Delta \rangle$$

with

1. $Q$ := Finite set of states
2. $I \subseteq Q$ := Set of initial states
3. $F \subseteq Q$ := Set of final states
4. $\Sigma$ := Finite set of symbols forming the input alphabet
5. $\Xi$ := Finite set of symbols forming the output alphabet
6. $\Delta \subseteq Q \times \Sigma^{*} \times Q \times \Xi^{*}$ := Set of state and output transitions

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

Figure 3.6: Finite transducer (generalized mealy)