0 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> http://www.kroening.com/publications/view-publications-bkossb2008-sttt.html