From small-overlap conditions to automatic semigroups

Details From small-overlap conditions to automatic semigroups From small-overlap conditions to automatic semigroups

2009-02-22

arxiv.org/abs/0902.3776v3

Mathematics

Rings and Algebras

33 pages, 9 figures, some mathematical errors were corrected in final section, few typos and exposition problems where fixed,

Scientific paper

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.

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