sat solver integration

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.

This study presents the first systematic exploration of whether large language models (LLMs) can autonomously construct a weightless MaxSAT solver from scratch using only research papers as input. The authors employ an iterative workflow in which ChatGPT extracts algorithmic insights, Codex generates initial code, and LLM-assisted auditing and revision refine the implementation, culminating in integration with an integer linear programming backend. A novel core-sequence lookahead strategy is introduced during this process. The resulting solver produces no incorrect outputs on benchmark instances, demonstrating the feasibility of LLM-driven development of complex constraint solvers. However, its performance remains inferior to that of state-of-the-art hand-optimized solvers, highlighting current limitations of LLMs in generating highly efficient algorithmic implementations.

This study systematically evaluates the solving performance of SAT and SMT solvers on ultra-large-scale Sudoku puzzles (25×25), focusing on solution efficiency and success rates across varying difficulty levels. Method: We construct a unified benchmarking framework integrating state-of-the-art SMT solvers (Z3, CVC5) and DPLL-based SAT solvers, coupled with a novel constraint-based Sudoku generator that supports controllable difficulty and structural diversity, alongside quantitative difficulty metrics. Contribution/Results: First, this work presents the first systematic empirical evaluation of SMT solvers on 25×25 Sudoku. Second, we propose a scalable, configurable Sudoku generator enabling precise difficulty tuning and enhanced puzzle diversity. Third, experimental results demonstrate that SMT solvers significantly outperform SAT solvers in both solving speed and robustness—particularly on harder instances—thereby empirically validating the benefits of theory-aware reasoning and high-level encodings for large-scale constraint satisfaction problems.

Modern CDCL SAT solvers suffer from low-quality initial variable assignments, while existing local-search preprocessing methods lack structural awareness of the underlying encoding. Method: This paper introduces the first large language model (LLM)-based, structure-aware framework for SAT solving. It parses Python-based SAT instance generators to infer semantic meaning and latent problem structure—including variable dependencies and constraint patterns—and automatically synthesizes domain-specific local-search algorithms tailored to each encoding type, thereby providing high-quality initial assignments for CDCL. Contribution/Results: Our approach overcomes the limitation of conventional preprocessing, which ignores structural priors, and achieves the first joint LLM-driven SAT encoding analysis and customized search algorithm generation. Evaluated on diverse SAT benchmark families, it significantly reduces total solving time and outperforms state-of-the-art heuristic preprocessing systems.

Existing evaluations of MaxSAT local search solvers overlook dynamic convergence behavior, focusing only on final solution quality and neglecting performance evolution over time. Method: We propose an empirical cumulative distribution function (ECDF)-based analysis method that quantifies solver convergence across multiple instances and time budgets, modeling high-variance anytime performance as an evaluable metric for the first time. We further integrate this ECDF-driven metric into the SMAC hyperparameter optimization framework to enable automated, convergence-aware solver configuration. Contribution/Results: Experimental results demonstrate that our approach yields more robust and efficient parameter configurations compared to conventional tuning strategies optimized solely for final solution quality. The ECDF-guided configuration significantly improves overall solver performance, revealing time-dependent solver strengths and enabling principled assessment of anytime behavior in MaxSAT solving.

This work addresses the challenge that Boolean satisfiability (SAT) solvers, due to their algorithmic sophistication and highly optimized data structures, often remain opaque to newcomers seeking to understand their inner workings and encoding efficacy. To bridge this gap, we present an open-source, web-based interactive teaching platform for SAT solving, featuring a progressive learning trajectory from naive backtracking through DPLL to full conflict-driven clause learning (CDCL). The platform supports literal-level breakpoint debugging, stateful assumption-based backtracking, real-time execution, and multi-mode automated solving. Notably, it integrates—for the first time—the two-watched-literals scheme, search trace visualization, and an extensible architecture, enabling fine-grained observation and manipulation of the solving process. Empirical use demonstrates that the system substantially enhances users’ comprehension of SAT algorithmic principles and their ability to analyze and optimize problem encodings.

This study addresses the challenge of the vast search space in solving and generating Hitori and Binairo logic puzzles by systematically comparing an optimized backtracking approach—integrating constraint propagation and heuristic variable ordering—with SAT-based methods. The work introduces the first unified framework for generating uniquely solvable instances of both puzzle types, enabling systematic benchmarking. This framework combines iterative connectivity checks with CNF encoding techniques. Experimental results demonstrate that constraint propagation substantially reduces search tree size; SAT solvers outperform other methods on Binairo, whereas the optimized backtracking algorithm achieves superior performance on Hitori. The proposed approaches provide efficient solutions for both puzzle generation and solving, while establishing a reproducible evaluation benchmark for future research.

This work addresses the challenge of efficiently and reliably importing large-scale logical certificates produced by SAT solvers into Lean 4 to formally verify the unsatisfiability of combinatorial problems. We present the first reflection-based LRAT checker implemented in Lean 4, which directly translates DIMACS formulas and LRAT certificates into Lean theorems without explicitly constructing massive proof terms. Our approach fully supports the internal composition of cube-and-conquer strategies and automatically synthesizes coverage completeness proofs. It significantly outperforms Mathlib’s existing proof-import mechanisms and achieves performance on par with the external checker cake_lpr when verifying large-scale instances such as the Schur number S(4)=44 and the Ramsey number R(4,4)=18, thereby enabling scalable and highly trustworthy automated verification of combinatorial theorems.