Circuits, coNP-completeness, and the groups of Richard Thompson
Jean-Camille Birget · arXiv (Cornell University) · 2003
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}.