PLCs – A counter PLC as a function

Any automaton can be seen as a function $ f: Sigma ^ * to {0,1 } $, namely, let $ f $ to be the characteristic function of the language that he accepts; or in other words, define $ f (x) = $ 1 if the word $ x $ is accepted by the automaton, otherwise $ f (x) = $ 0. This is true for only one finite automaton.