From Natural Language to Exact Cover: A Neuro-Symbolic Approach to Zebra Puzzles

Abstract

Chain-of-Thought (CoT) generation has substantially improved the performance of Large Language Models (LLMs) on complex reasoning tasks, including code generation, data analysis, and exam-style question answering. Despite these ad- vances, purely neural LLMs continue to struggle with elementary logical reason- ing problems and lack the determinism, soundness, and reliability characteristic of symbolic reasoning systems. Conversely, classical symbolic methods such as SAT solving and Exact Cover guarantee correctness and completeness, but re- quire problems to be expressed in highly specialized formal encodings, limiting their applicability to natural language inputs. In this work, we present a tightly integrated neuro-symbolic framework that bridges this gap by combining neural semantic parsing with deterministic constraint solving. Our approach leverages the relational extraction capabilities of modern LLMs to parse Zebra-style logic puzzles written in free-form text and translate the extracted constraints into struc- tured tool calls. These function calls assemble a formally specified Exact Cover instance, which is subsequently solved by a symbolic solver to ensure logically consistent solutions. We conduct a comprehensive empirical evaluation across multiple parameter scales, post-training paradigms, and LLM families. The re- sults on larger puzzles demonstrate that our hybrid approach consistently outper- forms strong plain neural baselines, including CoT prompting, as well as recent neuro-symbolic methods.