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.ICALP.2016.127
URN: urn:nbn:de:0030-drops-62624
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6262/
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Diekert, Volker ; Jez, Artur ; Kufleitner, Manfred

Solutions of Word Equations Over Partially Commutative Structures

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LIPIcs-ICALP-2016-127.pdf (0.4 MB)

Abstract

We give NSPACE(n*log(n)) algorithms solving the following decision problems. Satisfiability: Is the given equation over a free partially commutative monoid with involution (resp. a free partially commutative group) solvable? Finiteness: Are there only finitely many solutions of such an equation? PSPACE algorithms with worse complexities for the first problem are known, but so far, a PSPACE algorithm for the second problem was out of reach. Our results are much stronger: Given such an equation, its solutions form an EDT0L language effectively representable in NSPACE(n*log(n)). In particular, we give an effective description of the set of all solutions for equations with constraints in free partially commutative monoids and groups.

BibTeX - Entry

@InProceedings{diekert_et_al:LIPIcs:2016:6262,
  author =	{Volker Diekert and Artur Jez and Manfred Kufleitner},
  title =	{{Solutions of Word Equations Over Partially Commutative Structures}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{127:1--127:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6262},
  URN =		{urn:nbn:de:0030-drops-62624},
  doi =		{10.4230/LIPIcs.ICALP.2016.127},
  annote =	{Keywords: Word equations, EDT0L language, trace monoid, right-angled Artin group, partial commutation}
}

Keywords: Word equations, EDT0L language, trace monoid, right-angled Artin group, partial commutation
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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