Provably Complete Generalized Planning with LLMs

2026-09-22

AI Summary

该研究通过使用LLM生成Lean代码及证明，自动验证广义计划的完整性，解决以往需手动评估的问题。

Abstract

Generalized planning aims to compute a plan that solves all instances of a planning domain. Recent work has used LLMs to automatically generate and debug such generalized plans in the form of Python programs and achieved perfect test data coverage for several domains. However, whether these generalized plans are actually complete, i.e. solve all instances of the domain, could only be determined by manual evaluation. Here, we present an approach for automatically generating generalized plans in Lean together with proofs of their completeness relative to a specification of the domain constraints provided as input. We introduce a semantic-preserving PDDL-to-Lean conversion, and use an LLM to generate both the generalized plan and the formal proof that it solves every instance satisfying the domain constraints. The correctness of the completeness proof is determined by Lean's kernel. We evaluate our approach on 13 commonly used benchmark domains, using GPT-5.6-Sol as the LLM. For 12 of the domains we obtain generalized plans together with valid completeness proofs. This is a major advancement of the state of the art in automatic generalized-plan completeness proofs.

Problem

• Generalized Planning
• LLMs
• Completeness Proofs
• PDDL-to-Lean
• Automatic Generation

Innovation

• Generalized Planning
• LLMs
• Formal Proof
• PDDL-to-Lean Conversion
• Completeness Verification