Chain-Free String Constraints

We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new decidable fragment of string constraints, called weakly chaining string constraints, for which we show that the satisfiability problem is decidable. This fragment pushes the borders of decidability of string constraints by generalising the existing straight-line as well as the acyclic fragment of the string logic. We have developed a prototype implementation of our new decision procedure, and integrated it into an existing framework that uses CEGAR with under-approximation of string constraints based on flattening. This has led to an improvement of the running times as well as accuracy of the framework. We have demonstrated the competitiveness of the entire framework on benchmarks from the literature.