Groups with ALOGTIME-hard word problems and PSPACE-complete compressed word problems
Group Theory
2020-06-23 v5 Computational Complexity
Abstract
We give lower bounds on the complexity of the word problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, Grigorchuk's group and Thompson's groups, we prove that their word problem is -hard. For some of these groups (including Grigorchuk's group and Thompson's groups) we prove that the compressed word problem (which is equivalent to the circuit evaluation problem) is -complete.
Cite
@article{arxiv.1909.13781,
title = {Groups with ALOGTIME-hard word problems and PSPACE-complete compressed word problems},
author = {Laurent Bartholdi and Michael Figelius and Markus Lohrey and Armin Weiß},
journal= {arXiv preprint arXiv:1909.13781},
year = {2020}
}
Comments
A short version of the paper will appear in the Proceedings of the Computational Complexity Conference 2020