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Decidability and complexity of action-based temporal planning over dense time

2022; Elsevier BV; Volume: 307; Linguagem: Inglês

10.1016/j.artint.2022.103686

1872-7921

Nicola Gigante, Andrea Micheli, Angelo Montanari, Enrico Scala,

Semantic Web and Ontologies

In this paper, we study the computational complexity of action-based temporal planning interpreted over dense time. When time is assumed to be discrete, the problem is known to be EXPSPACE-complete. However, the official PDDL 2.1 semantics and many implementations interpret time as a dense domain. This work provides several results about the complexity of the problem, focusing on some particularly interesting cases: whether a minimum amount ε of separation between mutually exclusive events is given, in contrast to the separation being simply required to be non-zero, and whether or not actions are allowed to overlap already running instances of themselves. We prove the problem to be PSPACE-complete when self-overlap is forbidden, whereas, when it is allowed, it becomes EXPSPACE-complete with ε-separation and even undecidable with non-zero separation. These results clarify the computational consequences of different choices in the definition at the core of the PDDL 2.1 semantics, which have been vague until now.1