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DOI: 10.4230/LIPIcs.FSTTCS.2013.475
URN: urn:nbn:de:0030-drops-43948
URL: https://drops.dagstuhl.de/opus/volltexte/2013/4394/
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 | |
| Seminar: | IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013) | |
| Issue date: | 2013 | |
| Date of publication: | 10.12.2013 |
