André Schidler, Stefan Szeider

Extracting Problem Structure with LLMs for Optimized SAT Local Search

Introduction

Extracting problem structure with llms for optimized sat local search. LLMs extract problem structure from SAT encodings, automatically synthesizing specialized local search preprocessing algorithms. Optimize combinatorial search efficiency.

Abstract

Encoding combinatorial problems in terms of propositional satisfiability (SAT) enables utilization of highly efficient SAT solvers for combinatorial search. Local search preprocessing accelerates the SAT solver's search by providing high-quality starting points, a technique implemented in several modern SAT solvers. However, existing preprocessing methods employ generic strategies that fail to exploit the structural patterns inherent in problem encodings. This position paper proposes a novel paradigm wherein Large Language Models (LLMs) analyze problem encoding implementations to synthesize specialized preprocessing algorithms. The LLMs examine Python-based code to identify structural patterns, enabling the automatic generation of encoding-specific local search procedures. These procedures operate across all instances sharing the same encoding scheme rather than requiring instance-specific customization. Our preliminary empirical evaluation demonstrates effective automated algorithm synthesis for structure-aware SAT preprocessing, serving as a foundation for similar approaches across multiple domains of combinatorial optimization.

Review

This position paper introduces a compelling and novel approach to enhance SAT local search through the specialized application of Large Language Models (LLMs). The core innovation lies in moving beyond generic local search preprocessing strategies to synthesize *encoding-specific* algorithms by having LLMs analyze the problem encoding's implementation code. This addresses a significant limitation in current SAT solver acceleration techniques, which often overlook the inherent structural patterns within problem encodings. The proposed paradigm, which leverages LLMs to identify these patterns in Python-based code and automatically generate tailored preprocessing procedures, represents a promising direction for improving the efficiency of SAT solvers and, by extension, various combinatorial optimization tasks. A key strength of this work is its conceptual shift towards structure-aware preprocessing, offering a potential breakthrough in how SAT solvers are optimized. The idea of LLMs analyzing code to derive algorithmic insights is particularly intriguing, promising automated algorithm synthesis that can be applied across all instances sharing a particular encoding scheme without requiring instance-specific customization. This generalizability, once a preprocessing algorithm is generated for a given encoding, significantly enhances its practical utility. The preliminary empirical evaluation, though explicitly stated as foundational, provides an encouraging indication that automated, structure-aware algorithm synthesis for SAT preprocessing is indeed feasible and effective, laying the groundwork for further development and application. While the abstract presents a strong conceptual framework, the nature of it being a "position paper" with "preliminary empirical evaluation" naturally raises questions for future work. It would be valuable to understand the robustness of the LLMs in analyzing highly complex, non-trivial, or even poorly structured encoding implementations. The scalability of the LLM-driven synthesis process, both in terms of computational resources and the complexity of the algorithms it can generate, will be crucial. Future research should delve deeper into the breadth and depth of the empirical evaluation, perhaps comparing the synthesized algorithms against state-of-the-art generic and manually crafted specific heuristics on a wider range of benchmarks. Exploring the types of structural patterns LLMs are most adept at identifying and quantifying the performance gains across diverse problem domains would also strengthen the case for this innovative approach.

Full Text

Comments

You need to be logged in to post a comment.