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On the Structure of Solution Sets to Regular Word Equations

Authors Joel D. Day, Florin Manea

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Author Details

Joel D. Day
  • Loughborough University, UK
Florin Manea
  • Georg-August Universität, Göttingen, Germany

Funding

Florin Manea’s work was supported by the DFG grant MA 5725/2-1.

Cite As Get BibTex

Joel D. Day and Florin Manea. On the Structure of Solution Sets to Regular Word Equations. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 124:1-124:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.124

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics on words
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Quadratic Word Equations
  • Regular Word Equations
  • String Solving
  • NP

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