A characterization of those automata that structurally generate finite groups
Formal Languages and Automata Theory
2013-10-29 v1 Group Theory
Abstract
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.
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Cite
@article{arxiv.1310.7137,
title = {A characterization of those automata that structurally generate finite groups},
author = {Ines Klimann and Matthieu Picantin},
journal= {arXiv preprint arXiv:1310.7137},
year = {2013}
}