Abstract
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 | NX| x | NY | integer comparisons, where | Nx | and | Ny |, 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 min(|NX |, |NY|) integer comparisons, some in |NX| integer comparisons, and the others in |NY| integer comparisons. These linear time evaluation conditions enable the real-time applications to detect the relations efficiently.
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