An abstraction-based decision procedure for bit-vector arithmetic

Authors:
Randal E. Bryant;Daniel Kroening;Joël Ouaknine;Sanjit A. Seshia;Ofer Strichman;Bryan Brady
Affiliations:
Carnegie Mellon University, Pittsburgh, USA;Oxford University Computing Laboratory, Oxford, UK;Oxford University Computing Laboratory, Oxford, UK;University of California, Berkeley, USA;The Technion, Haifa, Israel;University of California, Berkeley, USA
Venue:
International Journal on Software Tools for Technology Transfer (STTT)
Year:
2009

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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.