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Bryant, R
Kroening, D
Ouaknine, J
Seshia, S
Strichman, O
Brady, B
2009
Deciding Bit-Vector Arithmetic with Abstraction
Software Tools for Technology Transfer (STTT)
Springer
11
2
95--104
<p>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 data-types. Our procedure alternates between generating under- and over-approximations of the original bit-vector formula. An under-approximation is obtained by a<br />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<br />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,<br />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<br />other competing decision procedures.</p>
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