Measuring closeness between Cayley automatic groups and automatic groups

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.

14 pages; minor corrections

References in corpus (2)

• Three Lectures on Automatic Structures
• Cayley automatic representations of wreath products

Cited by in corpus (5)

• Cayley Polynomial-Time Computable Groups
• Nonstandard Cayley automatic representations of fundamental groups
• String Compression in FA-Presentable Structures
• Extending the Synchronous Fellow Traveler Property
• Towards quantitative classification of Cayley automatic groups