Tightening BDD-based Approximate Reachability with SAT-based Clause Generalization

In the framework of symbolic model checking, BDD-based approximate reachability is potentially much more scalable than its exact counterpart. However, its practical applicability is highly limited by its static approach to abstraction, and the intrinsic difficulty to find an acceptable trade-off between accuracy and memory/time complexity. In this paper, we use SAT-based cube generalization, a core step of the IC3 model checking algorithm, in order to strengthen BDD-based representations of state sets. More specifically, we use cube generalization, in both its inductive and non-inductive versions, to tighten BDD-based over-approximate representations of state sets computed by Machine by Machine (MBM) and Frame by Frame (FBF) algorithms. The resulting approach benefits from the orthogonal power of BDD and CNF representations, and it improves the scalability and applicability in verification of BDD-based methods. Experimental results confirm that this approach can provide tighter representations of reachable state sets and more powerful fully BDD-based engines, as well as potential applications of BDDs as invariants or constraints in SAT-based model checking.