Combining Symmetry Reduction and Under-Approximation for Symbolic Model Checking

This work presents a collection of methods that integrate symmetry reduction and under-approximation with symbolic model checking in order to reduce space and time. The main objective of these methods is falsification . However, under certain conditions, they can provide verification as well. We first present algorithms that use symmetry reduction to perform on-the-fly model checking for temporal safety properties. These algorithms avoid building the orbit relation and choose representatives on-the-fly while computing the reachable states. We then extend these algorithms to check liveness properties as well. In addition, we introduce an iterative on-the-fly algorithm that builds subsets of the orbit relation rather than the full relation. Our methods are fully automatic once the user supplies some basic information about the symmetry in the verified system. Moreover, the methods are robust and work correctly even if the information supplied by the user is incorrect. Furthermore, the methods return correct results even when the computation of the symmetry reduction has not been completed due to memory or time explosion. We implemented our methods within the IBM model checker Rule-Base and compared their performance to that of RuleBase. In most cases, our algorithms outperformed RuleBase in both time and space.