🤖 AI Summary
MILP solvers’ outputs lack trustworthy verification in critical applications such as hardware verification, compiler optimization, and machine-assisted theorem proving. Method: This paper proposes the first formal verification framework for VIPR 1.0—a general-purpose certificate format—by fully encoding its inference rule system into unambiguous, SMT-expressible first-order logic formulas and constructing a solver-agnostic verifier compliant with the SMT-LIB standard to ensure algorithmic verifiability. Contribution/Results: The framework eliminates ambiguities inherent in the original VIPR specification and enables rigorous, implementation-independent validation of MILP certificates. Experimental evaluation on public benchmark suites confirms the verifier’s correctness and practical feasibility, demonstrating substantial improvements in both the rigor and generality of MILP certificate verification.
📝 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.
