Algorithmic Complexity of Correctness Testing in MC-Scheduling

Abstract

Previously, a lot of research has been done on scheduling a finite set of mixed criticality jobs with two levels of criticality on a single processor, which is also the subject of this work. It has been claimed that testing the correctness of solutions for this scheduling problem can be done in polynomial time. In this paper, we give a counter example to one of the lemmas used in that proof, reopening the question on whether the scheduling problem is in class NP. Taking into account our counter example, the authors who initially proved that correctness testing can be done in polynomial time published a fix to their proof. In the past, we proved that a previously existing correctness test is applicable for a quite general class of policies. From these results, for essentially the same class of policies, in this work we derive another correctness test, which transforms the policy to a new policy having a set of time-triggered tables, one for each criticality level. We show that the two policies are equivalent, in the sense that if one successfully schedules a jobs instance then so does the other. Thus the new transformed policy can be used for testing correctness of the original policy. We show that this correctness test has a lower algorithmic complexity than the existing test, due to the fact that the testing is done on only two static tables.