Undecidability of future timeline-based planning over dense temporal domains

The present work focuses on timeline-based planning over dense temporal domains. In automated planning, the temporal domain is commonly assumed to be discrete, the dense case being dealt with by resorting to some form of discretization. In the last years, the planning problem over dense temporal domains has been finally addressed both in the timeline-based setting and, very recently, in the action-based one. Dense timeline-based planning, in its full generality, has been shown to be undecidable. Decidability has been recovered by imposing suitable syntactic and/or semantic restrictions (the complexity of decidable fragments varies a lot, spanning from non-primitive recursive hardness to NP-completeness, passing through EXPSPACE- and PSPACE-completeness). In this paper, we proved that restricting to the future fragment is not enough to get decidability