Certified Branch-and-Bound MaxSAT Solving (Extended Version)

2025-11-13

AI Summary

Correctness verification of MaxSAT solvers has long lacked effective proof mechanisms, particularly within branch-and-bound frameworks where complex inferences—such as look-ahead strategies and pseudo-Boolean constraints encoded via multi-valued decision diagrams (MDDs)—resist generation of checkable certificates. Method: This paper introduces the first systematic extension of proof logging to an advanced branch-and-bound MaxSAT solver, MaxCDCL, supporting full verifiability for clausal encodings, MDD-based constraint representations, and look-ahead reasoning. We propose a low-overhead proof logging mechanism enabling end-to-end certificate generation. Contribution/Results: Our approach bridges the technical gap between MaxSAT’s optimization semantics and formal proof systems, enabling efficient and practical certificate generation. Experimental evaluation confirms its feasibility and scalability, significantly enhancing result trustworthiness. This work establishes the first formal verification foundation for high-assurance combinatorial optimization solvers.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Data transparency and provenance

Abstract

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.

Problem

• Ensuring correctness of Branch-and-Bound MaxSAT solvers through proof logging
• Certifying look-ahead methods and advanced clausal encodings in MaxSAT
• Implementing proof logging with limited overhead in MaxCDCL solver

Innovation

• Proof logging for Branch-and-Bound MaxSAT solving
• Certifying look-ahead methods in MaxSAT algorithms
• Advanced clausal encodings using Multi-Valued Decision Diagrams