AI Chat AI Image Generator AI Video Text to Speech

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

02/11/2019

∙

by J. C. Birget, et al.

∙

∙

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 n V 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.

research

∙ 09/30/2019

Groups with ALOGTIME-hard word problems and PSPACE-complete compressed word problems

We give lower bounds on the complexity of the word problem of certain no...

0 Laurent Bartholdi, et al. ∙

research

∙ 10/03/2021

The isomorphism problem for plain groups is in Σ_3^𝖯

Testing isomorphism of infinite groups is a classical topic, but from th...

0 Heiko Dietrich, et al. ∙

research

∙ 07/24/2023

Domino Snake Problems on Groups

In this article we study domino snake problems on finitely generated gro...

0 Nathalie Aubrun, et al. ∙

research

∙ 02/19/2021

Parallel algorithms for power circuits and the word problem of the Baumslag group

Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Wo...

0 Caroline Mattes, et al. ∙

research

∙ 01/15/2019

Random Subgroups of Rationals

This paper introduces and studies a notion of algorithmic randomness for...

0 Ziyuan Gao, et al. ∙

research

∙ 08/15/2022

Any strongly controllable group system or group shift or any linear block code is isomorphic to a generator group

Consider any sequence of finite groups A^t, where t takes values in an i...

0 Kenneth M. Mackenthun Jr, et al. ∙

research

∙ 10/08/2022

Some Tribonacci Conjectures

In a recent talk of Robbert Fokkink, some conjectures related to the inf...

0 Jeffrey Shallit, et al. ∙