On the Unusual Effectiveness of Type-aware Mutations for Testing SMT Solvers

We propose type-aware operator mutation, a simple, but unusually effective approach for testing SMT solvers. The key idea is to mutate operators of conforming types within the seed formulas to generate well-typed mutant formulas. These mutant formulas are then used as the test cases for SMT solvers. We realized type-aware operator mutation within the OpFuzz tool and used it to stress-test Z3 and CVC4, two state-of-the-art SMT solvers. Type-aware operator mutations are unusually effective: During nine months of extensive testing with OpFuzz, we reported 909 bugs in Z3 and CVC4, out of which 632 bugs were confirmed and 531 of the confirmed bugs were fixed by the developers. The detected bugs are highly diverse -- we found bugs of many different types (soundness bugs, invalid model bugs, crashes, etc.), logics and solver configurations. We have further conducted an in-depth study on the bugs found by OpFuzz. The study results show that the bugs found by OpFuzz are of high quality. Many of them affect core components of the SMT solvers' codebases, and some required major changes for the developers to fix. Among the 909 bugs found by OpFuzz, 130 were soundness bugs, the most critical bugs in SMT solvers, and 501 were in the default modes of the solvers. Notably, OpFuzz found 16 critical soundness bugs in CVC4, which has proved to be a very stable SMT solver.