License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2020.29
URN: urn:nbn:de:0030-drops-125814
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12581/
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Bartholdi, Laurent ; Figelius, Michael ; Lohrey, Markus ; Weiß, Armin

Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems

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LIPIcs-CCC-2020-29.pdf (0.7 MB)

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 ALOGTIME-hard. For some of these groups (including Grigorchuk’s group and Thompson’s groups) we prove that the circuit value problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.

BibTeX - Entry

@InProceedings{bartholdi_et_al:LIPIcs:2020:12581,
  author =	{Laurent Bartholdi and Michael Figelius and Markus Lohrey and Armin Wei{\ss}},
  title =	{{Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{29:1--29:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Shubhangi Saraf},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12581},
  URN =		{urn:nbn:de:0030-drops-125814},
  doi =		{10.4230/LIPIcs.CCC.2020.29},
  annote =	{Keywords: NC^1-hardness, word problem, G-programs, straight-line programs, non-solvable groups, self-similar groups, Thompson’s groups, Grigorchuk’s group}
}

Keywords: NC^1-hardness, word problem, G-programs, straight-line programs, non-solvable groups, self-similar groups, Thompson’s groups, Grigorchuk’s group
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020

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