On the Finiteness Problem for Automaton (Semi)Groups

  title={On the Finiteness Problem for Automaton (Semi)Groups},
  author={Ali Akhavi and Ines Klimann and S. Lombardy and J. Mairesse and Matthieu Picantin},
  • Ali Akhavi, Ines Klimann, +2 authors Matthieu Picantin
  • Published 2012
  • Mathematics, Computer Science
  • ArXiv
  • 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… CONTINUE READING
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