Automates réversibles: combinatoire, algèbre et topologie

Jean-Eric Pin (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be accepted by a reversible automaton. The first characterization gives a description of the subsets of the free group accepted by a reversible automaton that is somewhat reminiscent of Kleene's theorem. The second characterization is more combinatorial in nature. The decidability follows from the third -- algebraic -- characterization. The last and somewhat unexpected characterization is a topological description of our languages that solves an open problem about the finite-group topology of the free monoid.

Mots clés: automate réversible; topologie profinie; groupe libre

Domaines: Théorie des groupes [math.GR]; Mathématique discrète [cs.DM]

Jean-Eric Pin. Automates réversibles: combinatoire, algèbre et topologie. 2006. ⟨hal-00143942⟩