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Abstract The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to 𝒞-graph automatic by 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. The language is accepted by a finite state machine with two counters, and forms the basis of a 3-counter graph automatic structure for the group.
Groups Complexity Cryptology – de Gruyter
Published: Nov 1, 2015
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