From small-overlap conditions to automatic semigroups
Rings and Algebras
2010-09-21 v3
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.
Cite
@article{arxiv.0902.3776,
title = {From small-overlap conditions to automatic semigroups},
author = {Uri Weiss},
journal= {arXiv preprint arXiv:0902.3776},
year = {2010}
}
Comments
33 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