La representation ergodique d'un automate fini

AbstractWe study a special class of finite automata called reversible and defined by the following property: there exists a state such that, starting from it, both the automation and its (deterministic) reversal are strongly connected.The main tool to handle these automata is the ergodic representation which is mainly the Schützenberger matrix representation of the semigroup of the automaton over its minimal ideal. This representation allows the construction of a class of reversible automata: the so called homogeneous ones. This class is precisely the one obtained by considering a class of finite languages that are both prefix and suffix. We obtain here, by means of their automaton, a construction of these languages