TestMC: Testing Model Counters using Differential and Metamorphic Testing

Model counting is the problem for finding the number of solutions to a formula over a bounded universe. This is a classic problem in computer science that has seen many recent advances in techniques and tools that tackle it. These advances have led to applications of model counting in many domains, e.g., quantitative program analysis, reliability, and security. Given the sheer complexity of the underlying problem, today's model counters employ sophisticated algorithms and heuristics, which result in complex tools that must be heavily optimized. Therefore, establishing the correctness of implementations of model counters necessitates rigorous testing. This experience paper presents an empirical study on testing industrial strength model counters by applying the principles of differential and metamorphic testing together with bounded exhaustive input generation and input minimization. We embody these principles in the TestMC framework, and apply it to test four model counters, including three state-of-the-art model counters from three different classes. Specifically, we test the exact model counters projMC and dSharp, the probabilistic exact model counter Ganak, and the probabilistic approximate model counter ApproxMC. As subjects, we use three complementary test suites of input formulas. One suite consists of larger formulas that are derived from a wide range of real-world software design problems. The second suite consists of a bounded exhaustive set of small formulas that TestMC generated. The third suite consists of formulas generated using an off-the-shelf CNF fuzzer. TestMC found bugs in three of the four subject model counters. The bugs led to crashes, segmentation faults, incorrect model counts, and resource exhaustion by the solvers. Two of the tools were corrected subsequent to the bug reports we submitted based on our study, whereas the bugs we reported in the third tool were deemed by the tool authors to not require a fix.