Tree-based language complexity of Thompson's group F
Group Theory
2015-01-21 v2
Abstract
The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to C-graph automatic by Murray Elder and the first author raise the question of whether Thompson's group F is graph automatic. We define a language of normal forms based on the combinatorial "caret types" which arise when elements of F are considered as pairs of finite rooted binary trees, which we show to be accepted by a finite state machine with 2 counters, and forms the basis of a 3-counter graph automatic structure for the group.
Cite
@article{arxiv.1501.04315,
title = {Tree-based language complexity of Thompson's group F},
author = {Jennifer Taback and Sharif Younes},
journal= {arXiv preprint arXiv:1501.04315},
year = {2015}
}