If the input word is a word on then we have a finite input. If the input word is a word on then we have an infinite input. In the latter case is the run of an automaton also infinite. In case of an finite automaton with infinite input we will need instead of the set of final states additionally an acceptance condition.

In the case of a finite input word with we can say, that an automaton accepts word w if there exists a run with .

In case of an infinite input word with the run must fullfill certain acceptance conditions to be qualified as accepting the word (see below).

Gerd Doeben-Henisch 2010-03-03