Can LLMs Build a MaxSAT Solver from Papers? The CoreForge Experience

2026-07-16

AI Summary

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.

Abstract

We report on CoreForge, an experience in using large language models (LLMs) to build an unweighted MaxSAT solver from research papers rather than from an existing solver codebase. The project focuses on unsatisfiability-based MaxSAT algorithms and follows an iterative workflow that combines paper discussions with ChatGPT, implementation through Codex prompts, and repeated LLM-assisted code audits and revisions. Although the codebase implements several algorithms and solver components, our evaluation focuses on configurations that combine core-guided optimization, lightweight preprocessing, core minimization, integration with integer linear optimization backends, and a new core-sequence lookahead approach. Our experience suggests that LLMs can support solver implementation from papers, while requiring external validation, benchmarking, and human guidance. In our experiments, fuzzing and MaxSAT Evaluation instances did not reveal wrong answers in the tested configurations, although performance remains below the best hand-engineered MaxSAT solvers. We summarize what worked, what remained difficult, and the lessons for future LLM-assisted solver development.

Problem

• MaxSAT solver
• large language models
• unsatisfiability-based algorithms
• code generation from papers
• LLM-assisted development

Innovation

• Large Language Models
• MaxSAT Solver
• Core-Guided Optimization
• Core-Sequence Lookahead
• LLM-Assisted Code Generation