Dynamic Controllability of Conditional Simple Temporal Networks is PSPACE-complete

TL;DR

This paper proves that determining dynamic controllability of Conditional Simple Temporal Networks is a PSPACE-complete problem, resolving a long-standing open question in the field.

Contribution

It provides the first formal proof that checking dynamic controllability is PSPACE-complete, including constructions, algorithms, and theoretical arguments.

Findings

The problem is PSPACE-hard.

The problem is in PSPACE.

It settles the computational complexity of the problem.

Abstract

Even after the proposal of various solution algorithms, the precise computational complexity of checking whether a Conditional Temporal Network is Dynamically Controllable had still remained widely open. This issue gets settled in this paper which provides constructions, algorithms, and bridging lemmas and arguments to formally prove that: (1) the problem is PSPACE-hard, and (2) the problem lies in PSPACE.