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oai:drops-oai.dagstuhl.de:6457 2024-03-06T10:38:20Z ddc:004 open_access

Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups Godin, Thibault Klimann, Ines Burnside problem automaton groups reversibility orbit trees The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automaton. It has been proved that, for a connected automaton of size at most 3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite. In this paper, we extend these results to automata with bigger stateset, proving that, if a connected reversible automaton has a prime number of states, it cannot generate an infinite Burnside group. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thibault Godin and Ines Klimann 2016 Is Part Of LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2016.44 urn:nbn:de:0030-drops-64570 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.44 eng https://creativecommons.org/licenses/by/3.0/legalcode