Extracting Problem Structure with LLMs for Optimized SAT Local Search

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.