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.2020.124
URN: urn:nbn:de:0030-drops-125314
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12531/
Day, Joel D. ;
Manea, Florin
On the Structure of Solution Sets to Regular Word Equations
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}
}
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Keywords: |
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Quadratic Word Equations, Regular Word Equations, String Solving, NP |
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Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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29.06.2020 |
