Physics

Undecidable problem

Action (physics)

Mathematics

Algorithm

Decidability

PSPACE

Computational complexity theory

Semantics (computer science)

Programming language

Computer science

Quantum mechanics

Theoretical computer science

Time complexity

Artificial Intelligence

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

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