CertiStr: A Certified String Solver (technical report)

Abstract: Theories over strings are among the most heavily researched logical theories in the SMT community in the past decade, owing to the error-prone nature of string manipulations, which often leads to security vulnerabilities (e.g. cross-site scripting and code injection). The majority of the existing decision procedures and solvers for these theories are themselves intricate; they are complicated algorithmically, and also have to deal with a very rich vocabulary of operations. This has led to a plethora of bugs in implementation, which have for instance been discovered through fuzzing. In this paper, we present CertiStr, a certified implementation of a string constraint solver for the theory of strings with concatenation and regular constraints. CertiStr aims to solve string constraints using a forward-propagation algorithm based on symbolic representations of regular constraints as symbolic automata, which returns three results: sat, unsat, and unknown, and is guaranteed to terminate for the string constraints whose concatenation dependencies are acyclic. The implementation has been developed and proven correct in Isabelle/HOL, through which an effective solver in OCaml was generated. We demonstrate the effectiveness and efficiency of CertiStr against the standard Kaluza benchmark, in which 80.4% tests are in the string constraint fragment of CertiStr. Of these 80.4% tests, CertiStr can solve 83.5% (i.e. CertiStr returns sat or unsat) within 60s.