English

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.

Keywords

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

R2 v1 2026-06-21T12:14:11.870Z