Symmetric PMC model of diagnosis, b-matchings in graphs and fault identification in t-diagnosable systems

Abstract

A major breakthrough in the diagnosis of t-diagnosable systems occurred when Dahbura and Mason developed a diagnosis algorithm under the PMC model using the matching theory in bipartite graphs. In this paper we introduce a new testing model called the symmetric PMC(SPMC) model. Our main contributions are as follows: We prove that the diagnosability of an n-dimensional hypercube under the SPMC model is almost twice its diagnosability under the PMC model. We then show that the fault diagnosis problem for a t-diagnosable system under the SPMC model reduces to that of determining a maximum weighted b-matching in its diagnosis graph. Algorithm LABEL is then given to identify all the faulty vertices using the maximum b-matching of the diagnosis graph. Finally, using certain results from the theory of partitions of integers we establish the worst case complexity of our t-diagnosis algorithm. The complexity is much better than the worst case complexity of the Dahbura-Mason algorithm for the t-diagnosable problem under the PMC model.