SMT-based Model Checking for Recursive Programs

ABSTRACT. We present an SMT-based symbolic model checking algorithm for safety verification of recursive programs. The algorithm is modular and analyzes procedures individually. Unlike other SMT-based approaches, it maintains both "over-" and "under-approximations" of procedure summaries. Under-approximations are used to propagate information over procedure calls. Over-approximations are used to block infeasible counterexamples and detect convergence. We show that for programs and properties over a decidable theory, the algorithm is guaranteed to find a counterexample, if one exists. However, efficiency depends on an oracle for quantifier elimination (QE). For Boolean Programs, the algorithm is a polynomial decision procedure, matching the worst-case bounds of the best BDD-based algorithms. For Linear Arithmetic (integers and rationals), we give an efficient instantiation of the algorithm by applying QE "lazily". We use existing interpolation techniques to over-approximate QE and introduce "Model-Based Projection" to under-approximate QE. Empirical evaluation on SV-COMP benchmarks shows that our algorithm improves significantly on the state-of-the-art.