From small-overlap conditions to automatic semigroups
arXiv:0902.3776
Abstract
We study the connection between small-overlap conditions and automaticity of semigroups. We restrict the discussion to conditions that imply embeddability and under which each relation decomposes into at least seven pieces. For these hyperbolic-like conditions we show how to construct an automatic structure. Furthermore, we show that the naive approach of considering just geodesics fails in our case.
arXiv comment33 pages, 9 figures, some mathematical errors were corrected in final section, few typos and exposition problems where fixed, general structure and main result are unchanged