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arXiv · 1909.13781

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

Laurent Bartholdi·Michael Figelius·Markus Lohrey·Armin Weiß
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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 $\mathsf{NC}^1$-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 $\mathsf{PSPACE}$-complete.

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Laurent Bartholdi, Michael Figelius, Markus Lohrey, Armin Weiß. 2019-09-30. Groups with ALOGTIME-hard word problems and PSPACE-complete compressed word problems. https://arxiv.org/abs/1909.13781

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