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arXiv · 1310.7137

A characterization of those automata that structurally generate finite groups

Ines Klimann·Matthieu Picantin
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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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Ines Klimann, Matthieu Picantin. 2013-10-26. A characterization of those automata that structurally generate finite groups. https://arxiv.org/abs/1310.7137

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