Two-Round Diagnosability Measures for Multiprocessor Systems

In a multiprocessor system, as a key measure index for evaluating its reliability, diagnosability has attracted lots of attentions. Traditional diagnosability and conditional diagnosability have already been widely discussed. However, the existing diagnosability measures are not sufficiently comprehensive to address a large number of faulty nodes in a system. This article introduces a novel concept of diagnosability, called two-round diagnosability, which means that all faulty nodes can be identified by at most a one-round replacement (repairing the faulty nodes). The characterization of two-round t-diagnosable systems is provided; moreover, several important properties are also presented. Based on the abovementioned theories, for the n-dimensional hypercube (Q(n)), we show that its two-round diagnosability is (n(2) + n/2), which is (n + 1/2) times its classic diagnosability. Furthermore, a fault diagnosis algorithm is proposed to identify each node in the system under the PMC model. For Q(n), we prove that the proposed algorithm is the time complexity of O(n2(n)).