Rarely verification problems originate from bit-level descriptions. Yet, most of the verification technologies are based on bit blasting, i.e., reduction to boolean reasoning. In this paper we advocate reasoning at higher level of abstraction, within the theory of bit vectors (BV), where structural information (e.g. equalities, arithmetic functions) is not blasted into bits. Our approach relies on the lazy Satisfiability Modulo Theories (SMT) paradigm. We developed a satisfiability procedure for reasoning about bit vectors that carefully leverages on the power of boolean SAT solver to deal with components that are more naturally "boolean", and activates bit-vector reasoning whenever possible. The procedure has two distinguishing features. First, it relies on the on-line integration of a SAT solver with an incremental and backtrackable solver for BV that enables dynamical optimization of the reasoning about bit vectors; for instance, this is an improvement over static encoding methods which may generate smaller slices of bit-vector variables. Second, the solver for BV is layered (i.e., it privileges cheaper forms of reasoning), and it is based on a flexible use of term rewriting techniques. We evaluate our approach on a set of realistic industrial benchmarks, and demonstrate substantial improvements with respect to state-of-the-art boolean satisfiability solvers, as well as other decision procedures for SMT(BV).

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Abstract. We present several algorithms for simultaneous SAT (propositional satisfiability) based model checking of safety properties. More precisely, we focus on Bounded Model Checking and Temporal Induction methods for simultaneously verifying multiple safety properties on the same model. The most efficient among our proposed algorithms for model checking are based on a simultaneous propositional satisfiability procedure (SSAT for short), which we design for solving related propositional objectives simultaneously, by sharing the learned clauses and the search. The SSAT algorithm is fully incremental in the sense that all clauses learned while solving one objective can be reused for the remaining objectives. Furthermore, our SSAT algorithm ensures that the SSAT solver will never re-visit the same sub-space during the search, even if there are several satisfiability objectives, hence one traversal of the search space is enough. Finally, in SSAT all SAT objectives are watched simultaneously, thus we can solve several other SAT objectives when the search is oriented to solve a particular SAT objective first. Experimental results on Intel designs demonstrate that our new algorithms can be orders of magnitude faster than the previously known techniques in this domain.

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