DRAT-based Bit-Vector Proofs in CVC4

Abstract

Many state-of-the-art Satisfiability Modulo Theories (SMT) solvers for the theory of fixed-size bit-vectors employ an approach called bit-blasting, where a given formula is translated into a Boolean satisfiability (SAT) problem and delegated to a SAT solver. Consequently, producing bit-vector proofs in an SMT solver requires incorporating SAT proofs into its proof infrastructure. In this paper, we describe three approaches for integrating DRAT proofs generated by an off-the-shelf SAT solver into the proof infrastructure of the SMT solver CVC4 and explore their strengths and weaknesses. We implemented all three approaches using CryptoMiniSat as the SAT back-end for its bit-blasting engine and evaluated performance in terms of proof-production and proof-checking.

CoqQFBV: A Scalable Certified SMT Quantifier-Free Bit-Vector Solver

“…Such certificates demonstrate that the SMT QF BV query is reduced to a Boolean SAT query correctly and the corresponding SAT query is solved correctly. Although one can certify SAT query results with certificates from SAT solvers [24], it is not always easy to certify correct bit blasting due to complex arithmetic operations in SMT QF BV queries. Developing correct and efficient checkers for SMT QF BV certificates can be very challenging.…”