Abstract
We present a new decision procedure for finite-precision bit-vector arithmetic with arbitrary bit-vector operations. Such decision procedures are essential components of verifications systems, whether the domain of interest is hardware, such as in word-level bounded model-checking of circuits, or software, where one must often reason about programs with finite-precision datatypes. Our procedure alternates between generating under- and over-approximations of the original bit-vector formula. An under-approximation is obtained by a translation to propositional logic in which some bit-vector variables are encoded with fewer Boolean variables than their width. If the under-approximation is unsatisfiable, we use the unsatisfiable core to derive an over-approximation based on the subset of predicates that participated in the proof of unsatisfiability. If this over- approximation is satisfiable, the satisfying assignment guides the refinement of the previous under-approximation by increasing, for some bit-vector variables, the number of Boolean variables that encode them. We present experimental results that suggest that this abstraction-based approach can be considerably more efficient than directly invoking the SAT solver on the original formula as well as other competing decision procedures.
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B. Brady, R. E. Bryant, and S. A. Seshia were supported in part by SRC contract 1355.001. This research was also supported in part by the MARCO Gigascale Systems Research Center and by NSF grant CNS-0627734.
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Bryant, R.E., Kroening, D., Ouaknine, J. et al. An abstraction-based decision procedure for bit-vector arithmetic. Int J Softw Tools Technol Transfer 11, 95–104 (2009). https://doi.org/10.1007/s10009-009-0101-x
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DOI: https://doi.org/10.1007/s10009-009-0101-x