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Widespread use of string solvers in formal analysis of string-heavy programshas led to a growing demand for more efficient and reliable techniques whichcan be applied in this context, especially for real-world cases. Designing analgorithm for the (generally undecidable) satisfiability problem for systems ofstring constraints requires a thorough understanding of the structure ofconstraints present in the targeted cases. In this paper, we investigatebenchmarks presented in the literature containing regular expression membershippredicates, extract different first order logic theories, and prove theirdecidability, resp. undecidability. Notably, the most common theories inreal-world benchmarks are PSPACE-complete and directly lead to theimplementation of a more efficient algorithm to solving string constraints.

String Theories involving Regular Membership Predicates: From Practice to Theory and Back