Feasibility analysis of recurrent DAG tasks is PSPACE-hard

Abstract

We study a popular task model for scheduling parallel real-time tasks, where the internal parallelism of each task is modeled by a directed acyclic graph (DAG). We show that deciding the feasibility of a set of sporadically recurrent DAG tasks is hard for the complexity class PSPACE, thus ruling out approaches to this problem that rely on Integer Linear Programming or Satisfiability solvers (assuming $\text{NP}\ne \text{PSPACE}$).