Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Day, Joel D.; Manea, Florin https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-125314
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On the Structure of Solution Sets to Regular Word Equations

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Abstract

For quadratic word equations, there exists an algorithm based on rewriting rules which generates a directed graph describing all solutions to the equation. For regular word equations - those for which each variable occurs at most once on each side of the equation - we investigate the properties of this graph, such as bounds on its diameter, size, and DAG-width, as well as providing some insights into symmetries in its structure. As a consequence, we obtain a combinatorial proof that the problem of deciding whether a regular word equation has a solution is in NP.

BibTeX - Entry

@InProceedings{day_et_al:LIPIcs:2020:12531,
  author =	{Joel D. Day and Florin Manea},
  title =	{{On the Structure of Solution Sets to Regular Word Equations}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{124:1--124:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12531},
  URN =		{urn:nbn:de:0030-drops-125314},
  doi =		{10.4230/LIPIcs.ICALP.2020.124},
  annote =	{Keywords: Quadratic Word Equations, Regular Word Equations, String Solving, NP}
}

Keywords: Quadratic Word Equations, Regular Word Equations, String Solving, NP
Seminar: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue date: 2020
Date of publication: 29.06.2020


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