A language theoretic analysis of combings

Abstract

A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties of groups with combings in various formal language classes, and of the closure properties of the associated classes of groups. It generalises previous work, in particular of Epstein et al. and Bridson and Gilman.Comment: DVI and Post-Script files only, 21 pages. Submitted to International Journal of Algebra and Computatio