Fast and Verified UNSAT Certificate Checking

Abstract

We describe a formally verified checker for unsatisfiability certificates in the LRAT format, which can be run in parallel with the SAT solver, processing the certificate while it is being produced. It is implemented time and memory efficiently, thus increasing the trust in the SAT solver at low additional cost.The verification is done w.r.t. a grammar of the DIMACS format and a semantics of CNF formulas, down to the LLVM code of the checker. In this paper, we report on the checker and its design process using the Isabelle-LLVM stepwise refinement approach.