Quasi-automatic groups are asynchronously automatic

06/04/2019

∙

by   Benjamin Blanchette, et al.

∙

0

∙

share

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.