1. On the structure of solution-sets to regular word equations.
- Author
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Day, Joel D. and Manea, Florin
- Subjects
- *
QUADRATIC equations , *EQUATIONS , *ALGORITHMS , *SYMMETRY , *DECISION making - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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