(We can use emptiness algorithm to decide if )

Finite Automata with output

The definition of FA that we have already considered allows only two possible outputs is response to an input string, accept or reject. The definition can be extended so that the output can be chosen from some alphabet. Considering two different approaches to associate the output we have two different types of machines in the category- Moore machines and Mealy machines (They are named after the inventors). In a Moore machine the output is associated with the state, whereas in a Mealy machine the output is associated with the transition. Even though the two models look different, we can prove that they are equivalent.

Moore machines :

A Moore machine is a six-tuple

              where and q₀ are as in DFA . is the output alphabet and , is a mapping which gives the output associated with each state. Note that there is no final state and the input and output alphabet need not to be same.