# Complexity Bounds for the Controllability of Temporal Networks with Conditions, Disjunctions, and Uncertainty

## TL;DR

This paper establishes tight computational complexity bounds for checking controllability in advanced temporal networks with conditions, disjunctions, and uncertainty, showing all are solvable within PSPACE.

## Contribution

It provides the first tight complexity bounds for strong, weak, and dynamic controllability in complex temporal networks with multiple features.

## Key findings

- All controllability problems are in PSPACE.
- Subtle differences between network structures are identified.
- Complexity bounds are tightened for advanced models.

## Abstract

In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal constraints is consistent. While many of the simpler models have been well-studied from a computational complexity perspective, the algorithms developed for advanced models which combine features have very loose complexity bounds. In this paper, we provide tight completeness bounds for strong, weak, and dynamic controllability checking of temporal networks that have conditions, disjunctions, and temporal uncertainty. Our work exposes some of the subtle differences between these different structures and, remarkably, establishes a guarantee that all of these problems are computable in PSPACE.