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Journal Articles International Journal of Algebra and Computation Year : 2012

On the finiteness problem for automaton (semi)groups

Abstract

This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure.

Dates and versions

hal-00695445 , version 1 (08-05-2012)

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Cite

Ali Akhavi, Ines Klimann, Sylvain Lombardy, Jean Mairesse, Matthieu Picantin. On the finiteness problem for automaton (semi)groups. International Journal of Algebra and Computation, 2012, 22 (06), pp.1250052.1-1250052.26. ⟨10.1142/S021819671250052X⟩. ⟨hal-00695445⟩
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