Quasi-automatic groups are asynchronously automatic
Group Theory
2021-05-04 v1 Computational Complexity
Formal Languages and Automata Theory
Combinatorics
Abstract
A quasi-automatic semigroup is a finitely generated semigroup with a rational set of representatives such that the graph of right multiplication by any generator is a rational relation. A asynchronously automatic semigroup is a quasi-automatic semigroup for which these rational relations are also recognisable by two-tape automata. We show that when such a semigroup happens to be a group, the converse actually holds, meaning quasi-automatic groups are asynchronously automatic.
Cite
@article{arxiv.1906.01521,
title = {Quasi-automatic groups are asynchronously automatic},
author = {Benjamin Blanchette},
journal= {arXiv preprint arXiv:1906.01521},
year = {2021}
}
Comments
Short note, 5 pages, complementing a previous paper named Quasi-automatic Semigroups by Blanchette, Choffrut and Reutenauer