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.FSTTCS.2013.475
URN: urn:nbn:de:0030-drops-43948
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4394/
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Manea, Florin ; Müller, Mike ; Nowotka, Dirk

On the Pseudoperiodic Extension of u^l = v^m w^n

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Abstract

We investigate the solution set of the pseudoperiodic extension of the classical Lyndon and Sch\"utzenberger word equations. Consider u_1 ... u_l = v_1 ... v_m w_1 ... w_n, where u_i is in {u, theta(u)} for all 1 <= i <= l, v_j is in {v, theta(v)} for all 1 <= j <= m, w_k is in {w, theta(w)} for all 1 <= k <= n and u, v and w are variables, and theta is an antimorphic involution. A solution is called pseudoperiodic, if u,v,w are in {t, theta(t)}^+ for a word t. [Czeizler et al./I&C/2011] established that for small values of l, m, and n non-periodic solutions exist, and that for large enough values all solutions are pseudoperiodic. However, they leave a gap between those bounds which we close for a number of cases. Namely, we show that for l = 3 and either m,n >= 12 or m,n >= 5 and either m and n are not both even or not all u_i's are equal, all solutions are pseudoperiodic.

BibTeX - Entry

@InProceedings{manea_et_al:LIPIcs:2013:4394,
  author =	{Florin Manea and Mike M{\"u}ller and Dirk Nowotka},
  title =	{{On the Pseudoperiodic Extension of u^l = v^m w^n}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{475--486},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Anil Seth and Nisheeth K. Vishnoi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4394},
  URN =		{urn:nbn:de:0030-drops-43948},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.475},
  annote =	{Keywords: Word equations, Pseudoperiodicity, Lyndon-Sch{\"u}tzenberger equation}
}

Keywords: Word equations, Pseudoperiodicity, Lyndon-Schützenberger equation
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Issue Date: 2013
Date of publication: 10.12.2013

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