%0 Journal Article
%T A characterization of those automata that structurally generate finite groups
%A Ines Klimann
%A Matthieu Picantin
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1310.7137v1