AAAI 2026

January 22, 2026

Singapore, Singapore

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Modern planning systems utilize various plan representations - sequential, parallel, partially ordered (PO), and partial-order causal link (POCL) - each with different models for concurrency. These formalisms are often implicitly assumed to have the same base properties, particularly regarding makespan. We challenge this assumption, proving the relationship between them is fundamentally asymmetric. Our analysis shows conversions from plans with rigid concurrency layers (sequential, parallel) to those with flexible partial orders (PO, POCL) can preserve makespan. However, the reverse generally fails; the flexible orderings in PO/POCL plans can yield shorter makespans for solutions that cannot be represented in parallel plans without serialization. We prove that finding an optimal parallel representation for a given POCL plan is $\textsf{NP}$-complete, resolving a key question about their practical interchangeability. We also provide tight complexity bounds for makespan-bounded plan existence. Notably, our results disprove a claim in the literature that planning graph-based planners maximize concurrency by minimizing the critical path in derived PO plans.

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