Verifying the DPLL Algorithm in Dafny

Abstract

Modern high-performance SAT solvers quickly solve large satisfiability instances that occur in practice. If the instance is satisfiable, then the SAT solver can provide a witness which can be checked independently in the form of a satisfying truth assignment. However, if the instance is unsatisfiable, the certificates could be exponentially large or the SAT solver might not be able to output certificates. The implementation of the SAT solver should then be trusted not to contain bugs. However, the data structures and algorithms implemented by a typical high-performance SAT solver are complex enough to allow for subtle programming errors. To counter this issue, we build a verified SAT solver using the Dafny system. We discuss its implementation in the present article.