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

2019/02/11 by Birget, J. C.
#Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1902.03852

Abstract

We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n ≥ 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.

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