Thompson's group F is 1-counter graph automatic

Murray Elder 1  and Jennifer Taback 2
  • 1 School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan NSW 2308, Australia
  • 2 Department of Mathematics, Bowdoin College, Brunswick, ME 04011, USA


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.

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Groups – Complexity – Cryptology is a journal for speedy publication of articles in the areas of combinatorial and computational group theory, computer algebra, complexity theory, and cryptology. GCC primarily publishes research papers, but comprehensive and timely survey articles on a topic inside the scope of the journal are also welcome.