Measuring closeness between Cayley automatic groups and automatic groups (1804.02548v2)

Abstract: In this paper we introduce a way to estimate a level of closeness of Cayley automatic groups to the class of automatic groups using a certain numerical characteristic. We characterize Cayley automatic groups which are not automatic in terms of this numerical characteristic and then study it for the lamplighter group, the Baumslag--Solitar groups and the Heisenberg group.