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Circuits, coNP-completeness, and the groups of Richard Thompson

Jean-Camille Birget
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Abstract

We construct a finitely presented group with coNP-complete word problem, and a finitely generated simple group with coNP-complete word problem. These groups are represented as Thompson groups, hence as partial transformation groups of strings. The proof provides a simulation of combinational circuits by elements of the Thompson-Higman group G_{3,1}.

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Jean-Camille Birget. 2003-10-21. Circuits, coNP-completeness, and the groups of Richard Thompson. https://arxiv.org/abs/math/0310335

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