Abstract
System level diagnosis has been studied for many years since distributed systems became available. Preparata, et al. introduced the PMC model for identifying faulty units in a system using a graph, and at the same time gave the concept of t-diagnosability. Various measures of fault diagnosability have been proposed since then. In this paper, we provide characterization theorems for two measures of fault identification capability of a system which were introduced by Somani and Amin. We consider a structure of the system which has large capability for the other measures. In Somani's model for (k, t)-diagnosability, where a t-diagnosable system suffers at most k faults at each diagnosis step, we present a polynomial algorithm for obtaining the maximum t in order for the system to be (k, t)-diagnosable given k. In Amin's model for r-weak diagnosability, where a t-diagnosable system has at most one set of r faulty units tested by at least one normal unit, we examine a structure of the system to have the maximum r.
