Model reductions in MDG-based model checking

Multiway Decision Graphs (MDG) can symbolically represent abstract state machines (ASM). Since there is no preimage operation in MDG due to the presence of abstract state variables, all backward reduction algorithms can not be used in MDG. In this paper we propose a simple but powerful way to construct a reduced abstract transition system derived from the original ASM by using only the transition relations of the so-called property dependent state variables VP of the property P to be verified. It is easy to show that the abstract system so constructed strongly preserves P, and consequently the abstract system constructed using only a subset of VP weakly preserves P. The critical thing is how to select the subset of VP. We present here a heuristic iterative reduction algorithm for verifying the properties. At each iteration step, we trace further the property dependency graph and add a noncorrelated set of state variables to the current set of state variables to construct a more detailed model. The algorithm can handle both abstract and concrete state variables. It is completely automatic and succeeds in reducing the model and verifying properties where other tools fail.