It is not known whether Thompsons 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.
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