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DOI: 10.4230/LIPIcs.CCC.2020.29

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

Authors: Laurent Bartholdi, Michael Figelius, Markus Lohrey, and Armin Weiß

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

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.

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Laurent Bartholdi, Michael Figelius, Markus Lohrey, and Armin Weiß. Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 29:1-29:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bartholdi_et_al:LIPIcs.CCC.2020.29,
  author =	{Bartholdi, Laurent and Figelius, Michael and Lohrey, Markus and Wei{\ss}, Armin},
  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 =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.29},
  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}
}

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

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