A Decision Procedure for Subset Constraints over Regular Languages

Reasoning about string variables, in particular program inputs, is an important aspect of many program analyses and testing frameworks. Program inputs invariably arrive as strings, and are often manipulated using high-level string operations such as equality checks, regular expression matching, and string concatenation. It is difficult to reason about these operations because they are not well-integrated into current constraint solvers. We present a decision procedure that solves systems of equations over regular language variables. Given such a system of constraints, our algorithm finds satisfying assignments for the variables in the system. We define this problem formally and render a mechanized correctness proof of the core of the algorithm. We evaluate its scalability and practical utility by applying it to the problem of automatically finding inputs that cause SQL injection vulnerabilities.