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.
@InProceedings{day_et_al:LIPIcs.ICALP.2020.124, author = {Day, Joel D. and Manea, Florin}, 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 = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.124}, 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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