Approximating Predicate Images for Bit-Vector Logic

Daniel Kroening, Natasha Sharygina

Abstract: Predicate abstraction refinement is a successful technique for verifying large ANSI-C programs. However, computing the image of the predicates with respect to the transition relation is computationally expensive. Recent results have shown that predicate images can be computed by transforming a proof of a formula over integers into a Boolean formula that is satisfiable if and only if the original formula is satisfiable. However, the existing algorithms compute the closure of the proof rules that are used to axiomatize the logic, and thus, rely on the fact that the set of axioms is small. They are therefore limited to logics of low complexity, such as difference logic. We describe a proof-based algorithm that computes an over-approximation of the predicate image but in turn allows a rich set of axioms. The algorithm can be used to compute images of predicates using a combination of bit-vector logic, the theory of arrays, and pointer arithmetic. The proof-based approach can also be used to refine the image. We quantify the performance of the algorithm in comparison with a Das/Dill-like greedy incremental refinement of the image and a proof-based incremental refinement.