Thompson's group F is 1-counter graph automatic

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.