On the Structure of Solution Sets to Regular Word Equations
Joel D. Day, Florín Manea · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2020
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.