Certified MaxSAT Preprocessing

TL;DR

This paper introduces a method to certify the correctness of MaxSAT preprocessing techniques using proof logging, ensuring that reformulated instances preserve the original problem's optimal value, with practical feasibility demonstrated on benchmarks.

Contribution

It extends proof logging to MaxSAT preprocessing, providing formally verified certification that reformulated instances are equivalent to original problems.

Findings

Proof logging can certify MaxSAT preprocessing correctness.

The approach is practical on real-world benchmarks.

End-to-end proof checking guarantees solution validity.

Abstract

Building on the progress in Boolean satisfiability (SAT) solving over the last decades, maximum satisfiability (MaxSAT) has become a viable approach for solving NP-hard optimization problems, but ensuring correctness of MaxSAT solvers has remained an important concern. For SAT, this is largely a solved problem thanks to the use of proof logging, meaning that solvers emit machine-verifiable proofs of (un)satisfiability to certify correctness. However, for MaxSAT, proof logging solvers have started being developed only very recently. Moreover, these nascent efforts have only targeted the core solving process, ignoring the preprocessing phase where input problem instances can be substantially reformulated before being passed on to the solver proper. In this work, we demonstrate how pseudo-Boolean proof logging can be used to certify the correctness of a wide range of modern MaxSAT preprocessing techniques. By combining and extending the VeriPB and CakePB tools, we provide formally verified, end-to-end proof checking that the input and preprocessed output MaxSAT problem instances have the same optimal value. An extensive evaluation on applied MaxSAT benchmarks shows that our approach is feasible in practice.