Improved Bounded Model Checking for the Universal Fragment of CTL

SAT-based bounded model checking (BMC) has been introduced as a complementary technique to BDD-based symbolic model checking in recent years, and a lot of successful work has been done in this direction. The approach was first introduced by A. Biere \it et al. in checking linear temporal logic (LTL) formulae and then also adapted to check formulae of the universal fragment of computation tree logic (ACTL) by W. Penczek \it et al. As the efficiency of model checking is still an important issue, we present an improved BMC approach for ACTL based on Penczek's method. We consider two aspects of the approach. One is reduction of the number of variables and transitions in the k-model by distinguishing the temporal operator \it EX from the others. The other is simplification of the transformation of formulae by using uniform path encoding instead of a disjunction of all paths needed in the k-model. With these improvements, for an ACTL formula, the length of the final encoding of the formula in the worst case is reduced. The improved approach is implemented in the tool BMV and is compared with the original one by applying both to two well known examples, mutual exclusion and dining philosophers. The comparison shows the advantages of the improved approach with respect to the efficiency of model checking.