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Proceedings of the first LATIN conference, Saõ-Paulo : Brazil (1992)

On reversible automata

Jean-Eric Pin 1

(1992)

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 characterization relates reversible automata to the profinite group topology of the free monoid.

1 :	Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA)
	CNRS : UMR7089 – Université Paris VII - Paris Diderot

Équipe de recherche : Automates et Applications

Domaine

:

Informatique/Autre

Mots Clés : finite automata – reversible automata – free group – profinite topology

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Contributeur : Jean-Eric Pin <>

Soumis le : Jeudi 2 Mars 2006, 19:00:07

Dernière modification le : Jeudi 2 Mars 2006, 21:45:01