Wombit: A Portfolio Bit-Vector Solver Using Word-Level Propagation

Abstract

We develop an idea originally proposed by Michel and Van Hentenryck of how to perform bit-vector constraint propagation on the word level. Most operations are propagated in constant time, assuming the bit-vector fits in a machine word. In contrast, bit-vector SMT solvers usually solve bitvector problems by (ultimately) bit-blasting, that is, mapping the resulting operations to conjunctive normal form clauses, and using SAT technology to solve them. Bit-blasting generates intermediate variables which can be an advantage, as these can be searched on and learnt about. As each approach has advantages, it makes sense to try to combine them. In this paper, we describe an approach to bit-vector solving using word-level propagation with learning. We have designed alternative word-level propagators to Michel and Van Hentenryck's, and evaluated different variants of the approach. We have also experimented with different approaches to learning and back-jumping in the solver. Based on the insights gained, we have built a portfolio solver, Wombit, which essentially extends the STP bit-vector solver. Using machine learning techniques, the solver makes a judicious up-front decision about whether to use word-level propagation or fall back on bit-blasting.

Theory and Applications of Satisfiability Testing – SAT 2020

“…This approach has found application in verifying the equivalence of multiplication circuits [17], using signed and unsigned machine arithmetic. Further afield, but also motivated by the desire to bypass bit-blasting, efficient portfolio bit-vector solvers have been developed [25], combining learning with word-level propagators [20] that iteratively restrict the values that can be assigned to a bit-vector. In contrast to our work, the propagators are designed to run in constant time and make use of low-level bit-twiddling operations [26].…”