Extracting Problem Structure with LLMs for Optimized SAT Local Search

2025-01-24

AI Summary

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.

Technology Category

Constraint Satisfaction and Optimization: SatisfiabilitySearch and Optimization: Local SearchNatural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved informationSemantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactionsGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Local search preprocessing makes Conflict-Driven Clause Learning (CDCL) solvers faster by providing high-quality starting points and modern SAT solvers have incorporated this technique into their preprocessing steps. However, these tools rely on basic strategies that miss the structural patterns in problems. We present a method that applies Large Language Models (LLMs) to analyze Python-based encoding code. This reveals hidden structural patterns in how problems convert into SAT. Our method automatically generates specialized local search algorithms that find these patterns and use them to create strong initial assignments. This works for any problem instance from the same encoding type. Our tests show encouraging results, achieving faster solving times compared to baseline preprocessing systems.

Problem

• SAT Solving
• Local Search
• CDCL Solver

Innovation

• CDCL solvers
• large language models
• Python-encoded problems