Word equations in synergy with regular constraints (extended version) - Blahoudek, František; Chen, Yu-Fang; Chocholatý, David; Havlena, Vojtěch; Holík, Lukáš; Lengál, Ondřej; Síč, Juraj (Springer Nature, 2025)
We propose a new automata-based algorithm for solving string constraints that tightly integrates reasoning about equations and regular constraints. Exchanging information between the two allows an efficient pruning of generated combinatorial cases. The algorithm is based on a  novel language-based characterization of satisfiability of word equations with regular constraints. Namely, satisfiability of an equation is implied by its stability: the concatenation of the regular languages constraining variables on the left-hand side equals the concatenation of the languages on the right-hand side. It is complete for the chain-free string constraints. We experimentally show that our prototype implementation is competitive with the best string solvers and even superior on difficult examples.
Keywords: Word equations; regular constraints; string solving; finite automata