Automata and semigroups recognizing infinite words

Olivier Carton (1) , Dominique Perrin (2) , Jean-Eric Pin (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

This paper is a survey on the algebraic approach to the theory of automata accepting infinite words. We discuss the various acceptance modes (Büchi automata, Muller automata, transition automata, weak recognition by a finite semigroup, omega-semigroups) and prove their equivalence. We also give two algebraic proofs of McNaughton's theorem on the equivalence between Büchi and Muller automata. Finally, we present some recent work on prophetic automata and discuss its extension to transfinite words.

Domaines: Autre [cs.OH]; Logique en informatique [cs.LO]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Théorie des groupes [math.GR]

Olivier Carton, Dominique Perrin, Jean-Eric Pin. Automata and semigroups recognizing infinite words. J. Flum, E. Grädel and T. Wilke. Logic and Automata, History and perspectives, Amsterdam University Press, pp.585-596, 2007. ⟨hal-00340797⟩