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.STACS.2020.6
URN: urn:nbn:de:0030-drops-118674
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11867/
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Wächter, Jan Philipp ; Weiß, Armin

An Automaton Group with PSPACE-Complete Word Problem

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LIPIcs-STACS-2020-6.pdf (0.6 MB)

Abstract

We construct an automaton group with a PSPACE-complete word problem, proving a conjecture due to Steinberg. Additionally, the constructed group has a provably more difficult, namely EXPSPACE-complete, compressed word problem. Our construction directly simulates the computation of a Turing machine in an automaton group and, therefore, seems to be quite versatile. It combines two ideas: the first one is a construction used by D'Angeli, Rodaro and the first author to obtain an inverse automaton semigroup with a PSPACE-complete word problem and the second one is to utilize a construction used by Barrington to simulate circuits of bounded degree and logarithmic depth in the group of even permutations over five elements.

BibTeX - Entry

@InProceedings{wchter_et_al:LIPIcs:2020:11867,
  author =	{Jan Philipp W{\"a}chter and Armin Wei{\ss}},
  title =	{{An Automaton Group with PSPACE-Complete Word Problem}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11867},
  URN =		{urn:nbn:de:0030-drops-118674},
  doi =		{10.4230/LIPIcs.STACS.2020.6},
  annote =	{Keywords: automaton group, word problem, PSPACE, compressed word problem}
}

Keywords: automaton group, word problem, PSPACE, compressed word problem
Collection: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue Date: 2020
Date of publication: 04.03.2020

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