Satisfiability Modulo Theories for Verifying MILP Certificates

Abstract: Correctness of results from mixed-integer linear programming (MILP) solvers is critical, particularly in the context of applications such as hardware verification, compiler optimization, or machine-assisted theorem proving. To this end, VIPR 1.0 is the first recently proposed general certificate format for answers produced by MILP solvers. We design a schema to encode VIPR's inference rules as a ground formula that completely characterizes the validity of the algorithmic check, removing any ambiguities and imprecisions present in the specification. We implement a checker for VIPR certificates by expressing our ground formula with the Satisfiability Modulo Theory Library (SMT-LIB) and check its validity. Our approach is solver-agnostic, and we test its viability using benchmark instances found in the literature.