A set of synchronization relations between distributed nonatomic events was recently proposed to provide real-time applications with a fine level of discrimination in the specification of causality relations and synchronization conditions. For a pair of distributed nonatomic events X and Y, the evaluation of the synchronization relations requires jNXj jNY j integer comparisons, where jNXjand jNY j, respectively, are the number of nodes on which the two nonatomic events X and Y occur. In this paper, we show that this polynomial complexity of evaluation can by simplified using properties of partial orders to a linear complexity. Specifically, we show that most relations can be evaluated in minjNXj;jNY j integer comparisons, some in jNXj integer comparisons, and the others in jNY j integer comparisons. These linear time evaluation conditions enable the real-time applications to detect the relations efficiently.
Ajay D. Kshemkalyani