Symbolic reachability analysis based on SAT-solvers

Abstract

The introduction of symbolic model checking using Binary Decision Diagrams (BDDs) has led to a substantial extension of the class of systems that can be algorithmically verified. Although BDDs have played a crucial role in this success, they have some well-known drawbacks, such as requiring an externally supplied variable ordering and causing space blowups in certain applications. In a parallel development, SAT-solving procedures, such as Stålmarck's method or the Davis-Putnam procedure, have been used successfully in verifying very large industrial systems. These efforts have recently attracted the attention of the model checking community resulting in the notion of bounded model checking. In this paper, we show how to adapt standard algorithms for symbolic reachability analysis to work with SAT-solvers. The key element of our contribution is the combination of an algorithm that removes quantifiers over propositional variables and a simple representation that allows reuse of subformulas. The result will in principle allow many existing BDD-based algorithms to work with SAT-solvers. We show that even with our relatively simple techniques it is possible to verify systems that are known to be hard for BDD-based model checkers. © Springer-Verlag Berlin Heidelberg 2000.