On the Finiteness Problem for Automaton (Semi)groups
Formal Languages and Automata Theory
2013-01-11 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.1105.4725,
title = {On the Finiteness Problem for Automaton (Semi)groups},
author = {Ali Akhavi and Ines Klimann and Sylvain Lombardy and Jean Mairesse and Matthieu Picantin},
journal= {arXiv preprint arXiv:1105.4725},
year = {2013}
}