Decidability and Complexity of Timeline-based Planning over Dense Temporal Domains

In timeline-based planning, the planning domain is modeled as a set of independent, but interacting, components each one represented by a number of state variables, whose behavior over time (timelines) is governed by temporal constraints (synchronization rules). The temporal domain is typically assumed to be discrete. In this paper, we address decidability and complexity issues for timeline-based planning over dense temporal domains without resorting to any form of discretization. We first prove that the general problem is undecidable, and then we show that decidability can be recovered by constraining the logical structure of synchronization rules.