Provably Complete Generalized Planning with LLMs
Katharina Stein, Chaahat Jain, Jörg Hoffmann, Alexander Koller
cs.AI
Quick verdict
Kernel-checked completeness proofs for LLM-generated generalized plans on 12/13 PDDL domains; solid, but only relative to user-written validity constraints.
Summary
The paper targets generalized planning: computing a program that solves every instance of a PDDL domain, where prior LLM approaches (Silver et al. 2024; Stein et al. 2026) could establish completeness only by manual analysis. The authors present a Lean-based verification pipeline: a deterministic Python converter translates PDDL domains (restricted to conjunctive preconditions/effects with negation, no action costs) into Lean while preserving semantics; GPT-5.6-Sol implements a generalized plan following manually revised strategies from prior work; and the LLM then generates a completeness proof showing that for every instance satisfying user-provided validity constraints, the returned plan is applicable and achieves the goal. Anti-cheating safeguards bar custom notation/macros, verify the exact theorem statement, audit axiom dependencies, and re-verify the full module with a standalone checker. Across 13 benchmark domains, whole-proof generation succeeded on 7; an iterative sketch-based, declaration-level debugging loop resolved 5 of the remaining 6 (Transport failed, though its plan passed IPC Learning-track easy/medium tests). Runtimes span 9 minutes (Heavy) to 54 minutes (Rovers). Key limitations: the guarantees are relative to hand-authored constraints and invariants whose fidelity to the intended instance distribution is not machine-checked, and the planning strategies themselves are inherited from prior work rather than discovered by the LLM.
Review complete
Assessment at a glance
4
risk flags identified
● high 0
● medium 2
● low 2
4 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- The PDDL-to-Lean conversion is semantic-preserving, so kernel-accepted plan correctness transfers back to guarantees about the original PDDL (Lemmas 1-2, Theorem 1, Corollary 1).
- GPT-5.6-Sol can automatically generate both generalized plans and kernel-accepted Lean completeness proofs for 12 of 13 benchmark domains.
- A sketch-based iterative proof-debugging strategy succeeds where whole-proof generation fails, rescuing 5 of 6 hard domains.
- This is the first automatic generalized-plan completeness result at this scale; prior automation (Cui, Kuang and Liu 2023) was limited to simple domains and restricted instance sets.
Strengths
Machine-checked guarantees with concrete anti-cheating safeguards
Beyond kernel acceptance, the paper implements four concrete checks (Experiments/Preventing LLM cheating): rejecting custom notation/macros, matching the exact Listing-8 theorem statement, auditing axiom dependencies, and re-verifying the assembled module with Lean's standalone checker — directly addressing failure modes documented in Wang et al. 2026, Paglieri et al. 2026, and Ammanamanchi et al. 2026.
Formal PDDL-to-Lean bridge is carefully constructed
Definitions 1-2 (state/instance correspondence), Lemma 1 (action transitions commute), Lemma 2, Theorem 1 and Corollary 1 together justify that kernel acceptance implies correctness for the original PDDL, closing the gap between Lean encodings and planning semantics.
Large scale jump over prior automatic completeness results
Iterative sketch-based proof debugging is effective
Weaknesses
Guarantee is only relative to hand-authored validity constraints
Strategy discovery is not addressed
Restricted PDDL fragment and curated domain selection
Single-run, single-model evaluation without variance
No artifact release statement
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Review: Provably Complete Generalized Planning with LLMs
The remaining sections cover Methodology Assessment, Statistical Evidence, Results & Reproducibility, Limitations & Risks, and Verdict & Recommendations.
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Frequently asked questions
What does 'provably complete generalized planning' mean in this paper?
A generalized plan is a program mapping any task of a planning domain to a solution plan. Provably complete here means a machine-checked Lean proof exists that for every instance satisfying the specified validity constraints, the program returns an applicable plan achieving the goal — verified by Lean's kernel, not by testing on examples.
Which LLM was used and how well did it perform?
GPT-5.6-Sol (temperature 1, high reasoning). On 13 benchmark domains it produced generalized plans for all 13 and kernel-accepted completeness proofs for 12; only Transport failed after iterative proof debugging. Runtimes ranged from about 9 minutes (Heavy) to 54 minutes (Rovers).
What are the main limitations of the approach?
Completeness is proven only relative to user-written validity constraints and invariants whose fidelity to the intended instance distribution is not machine-checked; the supported PDDL fragment excludes action costs and numeric/derived features; solution strategies come from prior work rather than being invented by the LLM; and results are single runs on 13 domains with no code release stated.
How is this different from testing a generalized plan on benchmark instances?
Testing covers only the finite set of instances actually tried. A Lean proof covers the possibly infinite set of all instances satisfying the validity constraints; the paper formally bridges that proof back to PDDL semantics via a state/instance correspondence between PDDL and its Lean encoding.
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Figures 1-4 are present only as captions in the extracted text; their visual content could not be analyzed.
- Lean code excerpts contain rendering artifacts (broken spacing, unicode like '̸ ='); semantics were inferable but character-level fidelity is uncertain.
- No statement about code or artifact release appears in the extracted text; actual availability could not be verified.
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