Language Models as Higher-Order Planning Formalizers

LLMs can plan by either generating action sequences directly as a Planner or translating tasks into domain specific language for an external solver as a Formalizer. While most real-world tasks are asynchronous with non-uniform durations, concurrency, and execution-time constraints, existing benchmarks hardly cover them. We unify these asynchronous planning challenges under a single formulation and introduce the first three benchmarks that address each at scale. We conclude that the choice of formal representation primarily determines whether planning scales: as dependency graphs grow from 5 to 100 actions, Planner collapses from 96% to 5% plan accuracy and PDDL2.1 Formalizer from 13% to 0%, while CP-SAT Formalizer averages 94% and still achieves 83% at 100 actions. Faithfulness diagnostics show that PDDL2.1's predicate-based planning representation becomes brittle compared to general constraint satisfaction programs, when LLMs must keep predicates, effects, and goals consistent. Execution-time updates of planning constraints further degrade performance sharply (Planner 23.9%, PDDL2.1 0.7%, CP-SAT 46.1%), but a state-aware repair strategy that updates only event-induced constraints recovers CP-SAT Formalizer to 84.5%.

Large Language Models (LLMs) have shown promise for translating Natural Language (NL) planning descriptions into PDDL problem instances. However, standard evaluation criteria such as syntactic validity or planner success can substantially overestimate faithfulness to the described task: a generated problem may be parseable and solvable while misrepresenting the intended initial state, goal, object structure, or optimization target. This paper studies an end-to-end NL-to-PDDL pipeline that combines LLM generation, checks in terms of PDDL parsing, planning and validation, a domain-conformance checker, an LLM critic, and iterative repair. Fine-grained repair feedback is constructed from the domain description, the generated problem, the natural language problem description, and operational diagnostics. Reference-based comparisons against curated benchmark PDDL problem descriptions are used for post-hoc benchmark analysis, and these offline checks include renaming-invariant structural matching and semantic equivalence, where domain support is available. Across Planetarium, AutoPlanBench, and curated PDDL2.1 problems, results show that operational success and benchmark-reference reconstruction can diverge substantially. Results also show that structured repair can be useful, and that PDDL2.1 remains challenging for reference reconstruction, even when operational success improves.

Large Language Models (LLMs) have had a remarkable impact across many areas of machine learning. However, recent studies have shown that they struggle to reliably solve planning problems. At the same time, theoretical results have shown that transformers, the core architecture underlying modern LLMs, are Turing-complete. In this work, we investigate this apparent gap between the theoretical computational power of LLMs and their empirical planning performance. We propose Chain of Computation (COC), a computational architecture that places a transformer-based LM inside an iterative loop, leveraging its strength as a pattern-matching system. The COC uses a Structured Context Window (SCW) which provides a constant-sized context window with support for choosing which window is used at each planning step. Within this architecture, the LM is able to learn a planning policy, predicts the world model, and performs the arithmetic operations required during planning. We show that, when given an append-only SCW (resembling a Turing Machine tape), even relatively small LMs trained from scratch can learn planning policies and generalize from a small number of training instances within each planning domain, achieving success rates above 99.89% on BlocksWorld and the Pancake puzzle. Our analysis of failure cases in Tower of Hanoi (TOH) reveals that they arise from arithmetic operations or from encountering previously unseen tokens. We show that COC can solve TOH problem instances with up to 20 disks, requiring over 1 million actions, while requiring substantially less training data by either (1) planning with symbolical support for arithmetic or by (2) using a deterministic pushdown automaton (PDA) formulation for the SCW.