Solving Zebra Puzzles Using Constraint-Guided Multi-Agent Systems

TL;DR

This paper presents ZPS, a multi-agent system combining LLMs and theorem proving to effectively solve complex Zebra puzzles, outperforming standalone LLMs significantly.

Contribution

The introduction of ZPS, integrating LLMs with SMT solvers and feedback mechanisms, to improve solving complex logic puzzles like Zebra puzzles.

Findings

GPT-4 achieved 166% improvement in correct solutions

Automated grid puzzle grader proved reliable in user-study

ZPS outperformed individual LLMs in puzzle solving

Abstract

Prior research has enhanced the ability of Large Language Models (LLMs) to solve logic puzzles using techniques such as chain-of-thought prompting or introducing a symbolic representation. These frameworks are still usually insufficient to solve complicated logical problems, such as Zebra puzzles, due to the inherent complexity of translating natural language clues into logical statements. We introduce a multi-agent system, ZPS, that integrates LLMs with an off the shelf theorem prover. This system tackles the complex puzzle-solving task by breaking down the problem into smaller, manageable parts, generating SMT (Satisfiability Modulo Theories) code to solve them with a theorem prover, and using feedback between the agents to repeatedly improve their answers. We also introduce an automated grid puzzle grader to assess the correctness of our puzzle solutions and show that the automated grader is reliable by evaluating it in a user-study. Our approach shows improvement in all three LLMs we tested, with GPT-4 showing 166% improvement in the number of fully correct solutions.