Efficient Simplification of SAT Instances from Formal Verification of Microprocessors and Infinite-State Systems

Usage of SAT methods in Formal Verification is increasing [1]. Recently several preprocessors for SAT instances have been proposed [2], [3], [4]. Few of them have shown successes in some Formal Verification problems like Bounded Model Checking (BMC) and Equivalence Checking. As far as we know, none of them have been successful in reducing the complexity of microprocessor verification SAT instances. In [5,6], Velev and Bryant have concluded that applying a preprocessor (simplifier) to the CNF formulas resulting from realistic microprocessors is impractical, due to the large number of clauses-hundreds of thousands. In contrast, we show that a recent preprocessor, NiVER [7], results in solving SAT instances from Velev's microprocessor benchmark suite [8] in less time and space. We also explain the reason for the success of NiVER, while other preprocessors fail. We use the average number of implications by unit propagation of literals in the formula to estimate the cost of preprocessing. As far as we know, this paper is the first to estimate the cost of preprocessors and predict the usefulness of them. We also introduce and study a variant of NiVER, LiVER, that allows a limited increase in the formula size. Experimental results show that without NiVER preprocessing, some of the Velev's microprocessor verification SAT instances may not be solved due to huge memory or time requirements. On the experiments conducted so far, in unsatisfiable instances preprocessing resulted in upto 3x speed-up in time and solving few instances, which are otherwise aborted due to huge memory requirements. We also show the effect of preprocessing on SAT instances from UCLID [9] -a verification tool for infinite state systems.