Plans often change due to changes in the situation or our understanding of the situation. Sometimes, a feasible plan may not even exist, and identifying such infeasibilities is useful to determine when requirements need adjustment. Common planning approaches focus on efficient one-shot planning in feasible cases rather than updating domains or detecting infeasibility. We propose a Petri net reachability relaxation to enable robust invariant synthesis, efficient goal-unreachability detection, and helpful infeasibility explanations. We further leverage incremental constraint solvers to support goal and constraint updates. Empirically, compared to baselines, our system produces a comparable number of invariants, detects up to 2 times more infeasibilities, performs competitively in one-shot planning, and outperforms in sequential plan updates in the tested domains.
Figures & tables
Figure 1: Petri net structure for PDDL preconditions and effects. (a) variable in precondition (not in effect). (b) variable in effect (not in precondition). (c) variable in precondition and effect.
Figure 2: Two-literal invariants from our PN relaxation and baselines. All methods produce similar numbers of invariants.
Figure 3: Average infeasibility detection times over 10 iterations and counts. Absent data points exceeded a 10 -minute timeout or 8GiB memory limit. Dashes in the table indicates unsupported numeric domains for Mp and FD.
Figure 4: Average one-shot planning times over 10 iterations. The figures show the numbers of instances solved over time in numeric domains. Excluded data points exceeded the 10 -minute timeout or 8GiB memory limit.
Figure 5: Average cumulative planning times over 10 iterations for sequential planning. TMKit Gurobi outperforms the baselines in most sequences. Excluded data points exceeded the 30 -minute timeout or 8GiB memory limit.
Most research in planning focuses on generating a plan to achieve a desired set of goals. However, a goal specification can also be used to encode a property that should never hold, allowing a planner to identify a trace that would reach a flawed state. In such cases, the objective may shift to modifying the planning task to ensure that the flawed state is never reached, in other words, to make the planning task unsolvable. In this paper we introduce planning task shielding: the problem of detecting and repairing flaws in planning tasks. We propose three different approaches to solve these tasks, each aiming to minimize the number of modifications to the original actions that render the planning task unsolvable.
Alberto Pozanco, Pietro Totis, Marianela Morales +1
Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture that performs discrete symbolic reasoning while remaining fully differentiable. DSP maintains a feasibility channel (phi) that tracks constraint satisfaction evidence at each node, aggregates this into a global feasibility signal (Phi) through learned rule-weighted combination, and uses sparsemax attention to achieve exact-zero discrete rule selection. We integrate DSP into a Universal Cognitive Kernel (UCK) that combines graph attention with iterative constraint propagation. Evaluated on three constraint reasoning benchmarks -- graph reachability, Boolean satisfiability, and planning feasibility -- UCK+DSP achieves 97.4% accuracy on planning under 4x size generalization (vs. 59.7% for ablated baselines), 96.4% on SAT under 2x generalization, and maintains balanced performance on both positive and negative classes where standard neural approaches collapse. Ablation studies reveal that global phi aggregation is critical: removing it causes accuracy to drop from 98% to 64%. The learned phi signal exhibits interpretable semantics, with values of +18 for feasible cases and -13 for infeasible cases emerging without supervision.
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.
André G. Pereira, Augusto B. Corrêa, Felipe Meneguzzi +1
Federal University of Rio Grande do Sul Brazil · University of Oxford United Kingdom · University of Aberdeen United Kingdom +1