# Undecidability of future timeline-based planning over dense temporal domains

## TL;DR

This paper proves that timeline-based planning over dense temporal domains remains undecidable even when restricting to future semantics, highlighting fundamental computational limitations in this planning approach.

## Contribution

It extends previous undecidability results by showing that future semantics of trigger rules also lead to undecidability in timeline-based planning.

## Key findings

- Undecidability holds under future semantics of trigger rules.
- Dense-time timeline-based planning is undecidable even with restricted semantics.
- The result emphasizes inherent computational limits in expressive planning models.

## Abstract

Planning is one of the most studied problems in computer science. In this paper, we consider the timeline-based approach, where the domain is modeled by a set of independent, but interacting, components, identified by a set of state variables, whose behavior over time (timelines) is governed by a set of temporal constraints (synchronization rules). Timeline-based planning in the dense-time setting has been recently shown to be undecidable in the general case, and undecidability relies on the high expressiveness of the trigger synchronization rules. In this paper, we strengthen the previous negative result by showing that undecidability already holds under the future semantics of the trigger rules which limits the comparison to temporal contexts in the future with respect to the trigger.