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Groups with ALOGTIME-hard Word Problems and PSPACE-complete Compressed Word Problems

Published:01 February 2023Publication History
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Abstract

We give lower bounds on the complexity of the word problem for a large class of non-solvable infinite groups that we call strongly efficiently non-solvable groups. This class includes free groups, Grigorchuk’s group, and Thompson’s groups. We prove that these groups have an NC1-hard word problem and that for some of them (including Grigorchuk’s group and Thompson’s groups) the compressed word problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.

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          cover image ACM Transactions on Computation Theory
          ACM Transactions on Computation Theory  Volume 14, Issue 3-4
          December 2022
          122 pages
          ISSN:1942-3454
          EISSN:1942-3462
          DOI:10.1145/3582881
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          Publication History

          • Published: 1 February 2023
          • Online AM: 1 December 2022
          • Accepted: 24 October 2022
          • Revised: 10 October 2022
          • Received: 29 August 2021
          Published in toct Volume 14, Issue 3-4

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