Cayley graph automatic groups are not necessarily cayley graph biautomatic

Authors:
Alexei Miasnikov;Zoran Šunić
Affiliations:
Department of Mathematical Sciences, Stevens Institute, Hoboken, NJ;Department of Mathematics, Texas A&M University, TX
Venue:
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Year:
2012

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Abstract

We show that there are Cayley graph automatic groups that are not Cayley graph biautomatic. In addition, we show that there are Cayley graph automatic groups with undecidable Conjugacy Problem and that the Isomorphism Problem is undecidable in the class of Cayley graph automatic groups.