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Conference Papers Lecture Notes in Computer Science Year : 2014

A characterization of those automata that structurally generate finite groups

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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hal-00877087 , version 1 (25-10-2013)

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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⟩

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