Word Equations in Synergy with Regular Constraints (Technical Report)

TL;DR

This paper introduces a novel, efficient algorithm for solving combined word equations and regular constraints, demonstrating superior performance and completeness for a specific fragment, advancing string solving techniques.

Contribution

It presents a new integrated approach and algorithm for solving word equations with regular constraints, improving efficiency and completeness over existing methods.

Findings

Prototype outperforms existing solvers on difficult examples.

Algorithm is complete for chain-free constraints fragment.

Achieves faster solving times with fewer timeouts.

Abstract

When eating spaghetti, one should have the sauce and noodles mixed instead of eating them separately. We argue that also in string solving, word equations and regular constraints are better mixed together than approached separately as in most current string solvers. We propose a fast algorithm, complete for the fragment of chain-free constraints, in which word equations and regular constraints are tightly integrated and exchange information, efficiently pruning the cases generated by each other and limiting possible combinatorial explosion. The algorithm is based on a novel language-based characterisation of satisfiability of word equations with regular constraints. We experimentally show that our prototype implementation is competitive with the best string solvers and even superior in that it is the fastest on difficult examples and has the least number of timeouts.