EDF-schedulability of synchronous periodic task systems is coNP-hard

In the synchronous periodic task model, a set τ1, …, τn of tasks is given, each releasing jobs of running time ci with relative deadline di, at each integer multiple of the period pi. It is a classical result that Earliest Deadline First (EDF) is an optimal preemptive uniprocessor scheduling policy. For constrained deadlines, i.e. di ≤ pi, the EDF-schedule is feasible if and only if Though an enormous amount of literature deals with this topic, the complexity status of this test has remained unknown. We prove that testing EDF-schedulability of such a task system is (weakly) coNP-hard. This solves Problem 2 from the survey “Open Problems in Real-time Scheduling” by Baruah & Pruhs. The hardness result is achieved by applying recent results on inapproximability of Diophantine approximation.