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Quasi-automatic groups are asynchronously automatic (1906.01521v1)
Published 4 Jun 2019 in math.GR, cs.CC, cs.FL, and math.CO
Abstract: A quasi-automatic semigroup is a finitely generated semigroup with a rational set of representatives such that the graph of right multiplication by any generator is a rational relation. A asynchronously automatic semigroup is a quasi-automatic semigroup for which these rational relations are also recognisable by two-tape automata. We show that when such a semigroup happens to be a group, the converse actually holds, meaning quasi-automatic groups are asynchronously automatic.