Using adaptive symmetry reduction for LTL model checking

The main difficulty all model checking tools encounter with is the state explosion problem: the state space of a system model grows exponentially with the number of processes of the system. Various techniques (abstraction, partial order reduction, symmetry reduction, etc.) have been developed to cope with this problem by taking advantages of specific algebraic features of particular models. Symmetry reduction, for example, is based on the fact that models M and M/G are bisimilar for any automorphism group G of a model M . The state space of M/G is the set of all orbits of M w.r.t. G. Therefore, the size of M/G may be substantially less than that of M . Unfortunately, given an arbitrary model M , it is not easy to compute a nontrivial automorphism group G. To overcome this obstacle the author of [4] offered an adaptive symmetry reduction (ASR) technique which gave a possibility to benefit from symmetry in state reachability analysis without resorting explicitly to the orbits. The key idea of this approach is to start a reachability checking assuming the perfect symmetry of a transition system and refine this assumption by tracking the changes that violate the estimated symmetry. At every step of the analysis the state space is divided into meta-states — the sets of presumably symmetric states. In the course of the checking meta-states are split on-demand to conform the transitions of the system. We found that ASR is applicable to LTL model checking as well. The main contribution of our paper is a new automata-theoretic approach to LTL model checking which combines ASR and double depth-first search algorithm (DDFS) for checking the emptiness of Büchi automata.