When both Grounding and not Grounding are Bad -- A Partially Grounded Encoding of Planning into SAT (Extended Version)

Grounding is a critical step in classical planning, yet it often becomes a computational bottleneck due to the exponential growth in grounded actions and atoms as task size increases. Recent advances in partial grounding have addressed this challenge by incrementally grounding only the most promising operators, guided by predictive models. However, these approaches primarily rely on relational features or learned embeddings and do not leverage the textual and structural cues present in PDDL descriptions. We propose SPG-LLM, which uses LLMs to analyze the domain and problem files to heuristically identify potentially irrelevant objects, actions, and predicates prior to grounding, significantly reducing the size of the grounded task. Across seven hard-to-ground benchmarks, SPG-LLM achieves faster grounding-often by orders of magnitude-while delivering comparable or better plan costs in some domains.

Factored tasks are a classical planning representation that extends SAS+ with limited forms of disjunctive preconditions, conditional effects, and angelic nondeterminism. This allows for a more compact representation of tasks than traditional formalisms such as STRIPS or SAS+, and supports a wide range of task transformations. However, existing planning approaches for factored tasks have been limited to heuristic search methods. In this work, we investigate how to encode factored tasks in SAT. We propose several ways to encode the tasks, focusing on different strategies for translating the factored transition relation into propositional logic. We also analyze how to exploit parallelism at various levels in this setting and study the impact of common task transformations on the performance of SAT-based planners.

Frontier large language models (LLMs) can generate heuristic functions that guide search to achieve state-of-the-art performance in satisficing planning, where any plan is acceptable. However, these heuristics are not guaranteed to be admissible and can lead to suboptimal plans. We introduce LeanPlan, the first planning system that finds optimal plans with LLM-generated heuristics whose admissibility is machine-checked. Given a domain description and training tasks, an agentic loop uses planner feedback to iteratively improve a reusable domain-specific heuristic, its admissibility proof and the required domain assumptions. LeanPlan implements the heuristic, its proof and an efficient planner with machine-checked grounding and search in Lean 4. We evaluate LeanPlan on ten domains from the International Planning Competition and three new domains, using test tasks with up to 57 times as many objects as the training tasks. With GPT-5.6 Sol in the agentic loop, we successfully generate heuristics and admissibility proofs for all these domains. With the resulting heuristics, LeanPlan usually expands fewer states than the state-of-the-art Scorpion planner and solves more tasks overall.