SAT Based Predicate Abstraction for Hardware Verification

Predicate abstraction is an important technique for extracting compact finite state models from large or infinite state systems. Predicate abstraction uses decision procedures to compute a model which is amenable to model checking, and has been used successfully for software verification. Little work however has been done on applying predicate abstraction to large scale finite state systems, most notably, hardware, where the decision procedures are SAT solvers. We consider predicate abstraction for hardware in the framework of CounterexampleGuided Abstraction Refinement where in the course of verification, the abstract model has to be repeatedly refined. The goal of the refinement is to eliminate spurious behavior in the abstract model which is not present in the original model, and gives rise to false negatives (spurious counterexamples). In this paper, we present two efficient SAT-based algorithms to refine abstract hardware models which deal with spurious transitions and spurious counterexamples respectively. Both algorithms make use of the conflict graphs generated by SAT solvers. The first algorithm extracts constraints from the conflict graphs which are used to make the abstract model more accurate. Once an abstract transition is determined to be spurious, our algorithm does not need to make any additional calls to SAT solver. Our second algorithm generates a compact predicate which eliminates a spurious counterexample. This algorithm uses the conflict graphs to identify the important concrete variables that render the counterexample spurious, creates an additional predicate over these concrete variables, and adds it to the abstract model. Experiments over hardware designs with several thousands of registers demonstrate the effectiveness of our methods. This research was sponsored by the Semiconductor Research Corporation (SRC) under contract no. 99-TJ-684, the National Science Foundation (NSF) under grant no. CCR-9803774, the Office of Naval Research (ONR), the Naval Research Laboratory (NRL) under contract no. N00014-01-1-0796, and by the Defense Advanced Research Projects Agency, and the Army Research Office (ARO) under contract no. DAAD19-01-1-0485, the General Motors Collaborative Research Lab at CMU, the Austrian Science Fund Project N Z29-N04, and the EU Research and Training Network GAMES. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of SRC, NSF, ONR, NRL, DOD, ARO, or the U.S. government.