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.MFCS.2019.44
URN: urn:nbn:de:0030-drops-109889
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10988/
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Day, Joel D. ; Manea, Florin ; Nowotka, Dirk

Upper Bounds on the Length of Minimal Solutions to Certain Quadratic Word Equations

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LIPIcs-MFCS-2019-44.pdf (0.5 MB)

Abstract

It is a long standing conjecture that the problem of deciding whether a quadratic word equation has a solution is in NP. It has also been conjectured that the length of a minimal solution to a quadratic equation is at most exponential in the length of the equation, with the latter conjecture implying the former. We show that both conjectures hold for some natural subclasses of quadratic equations, namely the classes of regular-reversed, k-ordered, and variable-sparse quadratic equations. We also discuss a connection of our techniques to the topic of unavoidable patterns, and the possibility of exploiting this connection to produce further similar results.

BibTeX - Entry

@InProceedings{day_et_al:LIPIcs:2019:10988,
  author =	{Joel D. Day and Florin Manea and Dirk Nowotka},
  title =	{{Upper Bounds on the Length of Minimal Solutions to Certain Quadratic Word Equations}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10988},
  URN =		{urn:nbn:de:0030-drops-109889},
  doi =		{10.4230/LIPIcs.MFCS.2019.44},
  annote =	{Keywords: Quadratic Word Equations, Length Upper Bounds, NP, Unavoidable Patterns}
}

Keywords: Quadratic Word Equations, Length Upper Bounds, NP, Unavoidable Patterns
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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