Thompson's group F is 1-counter graph automatic
Group Theory
2015-01-21 v1 Formal Languages and Automata Theory
Abstract
It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to C-graph automatic by the authors, a compelling question is whether F is graph automatic or C-graph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1-counter graph automatic structure for F based on the standard infinite normal form for group elements.
Cite
@article{arxiv.1501.04313,
title = {Thompson's group F is 1-counter graph automatic},
author = {Murray Elder and Jennifer Taback},
journal= {arXiv preprint arXiv:1501.04313},
year = {2015}
}