Solving String Constraints with Streaming String Transducers

Abstract

We present a procedure to solve the satisfiability problem of string constraints consisting of (i) string concatenation and rational transductions of string variables restricted to be in the “straight-line” fragment, (ii) regular constraints to string variables, and (iii) integer constraints involving the length of string variables. We represent each atomic string constraint by a streaming string transducer. By the sequential composition of streaming string transducers, we obtain a single streaming string transducer. The input straight-line constraint is satisfiable if and only if the domain of the composed streaming string transducer is not empty. In addition, by calculating the Parikh image of the composed streaming string transducers, we can represent the constraints among the length of string variables as a semi-linear set. Then the integer constraints together with the Parikh image can be solved by existing SMT solvers. We have implemented this procedure and performed experiments on several string constraints. Our implementation is slower than other solvers for general cases but performs better for some special cases.