Thompson's group F is 1-counter graph automatic

TL;DR

This paper demonstrates that Thompson's group F has a 1-counter graph automatic structure, extending the understanding of its algebraic properties through advanced automata theory.

Contribution

The authors construct a 1-counter graph automatic structure for Thompson's group F using the standard infinite normal form, advancing the automata-based analysis of the group.

Findings

Thompson's group F is shown to be 1-counter graph automatic.

The construction uses the standard infinite normal form.

This extends the class of automata-recognizable structures for F.

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.