The word problem of the Brin-Thompson group is coNP-complete

Abstract

We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n \ge 2. It is known that the groups nV are an infinite family of infinite, finitely presented, simple groups. We also prove that the word problem of the Thompson group V over a certain infinite set of generators, related to boolean circuits, is coNP-complete.

38 pages

References in corpus (2)

• Circuits, coNP-completeness, and the groups of Richard Thompson
• Rigidity properties of full groups of pseudogroups over the Cantor set