A characterization of those automata that structurally generate finite groups

Ines Klimann (1) , Matthieu Picantin (1)

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

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper.

Keywords: automaton groups; Mealy automata; finiteness problem

Domains: Formal Languages and Automata Theory [cs.FL]; Group Theory [math.GR]

Ines Klimann, Matthieu Picantin. A characterization of those automata that structurally generate finite groups. 11th Latin American Theoretical INformatics Symposium (LATIN 2014), 2014, Uruguay. pp.180--189. ⟨hal-00877087⟩