Equivalence of infinite behavior of finite automata

AbstractGiven a finite automaton, its infinite behavior is defined by Büchi (1962), Eilenberg (1974) and McNaughton (1966) as the set of all infinite sequences of letters which label paths passing infinitely many times through a given subset of states. Two finite automata are said to be equivalent when their infinite behaviors are equal.In this paper we give a necessary and sufficient condition of equivalence, which uses considerations over finite behaviors only. An algorithm for the general case (deterministic or not) is given; its time and space complexity is better than any other existent method