Certified Branch-and-Bound MaxSAT Solving

Over the past few decades, combinatorial solvers have seen remarkable performance improvements, enabling their practical use in real-world applications. In some of these applications, ensuring the correctness of the solver's output is critical. However, the complexity of modern solvers makes them susceptible to bugs in their source code. In the domain of satisfiability checking (SAT), this issue has been addressed through proof logging, where the solver generates a formal proof of the correctness of its answer. For more expressive problems like MaxSAT, the optimization variant of SAT, proof logging had not seen a comparable breakthrough until recently. In this paper, we show how to achieve proof logging for state-of-the-art techniques in Branch-and-Bound MaxSAT solving. This includes certifying look-ahead methods used in such algorithms as well as advanced clausal encodings of pseudo-Boolean constraints based on so-called Multi-Valued Decision Diagrams (MDDs). We implement these ideas in MaxCDCL, the dominant branch-and-bound solver, and experimentally demonstrate that proof logging is feasible with limited overhead, while proof checking remains a challenge. This is an extended version of a paper that will be published in the proceedings of AAAI 2026 (Vandesande et al., 2026) . It extends the published version with a technical appendix including proofs and more details.