On a generalization of the self-implicating structures in diagnosable systems

It is known that among the diagnosable systems modeled as in the model of F.P. Preparata et al. (1967), there exist several subclasses of systems that can be diagnosed more efficiently than the general case. These subclasses include D(n, t, x) systems, self-implicating systems, and systems having connection assignment digraph of node connectivity t, among others. It has been shown that some of these classes are unrelated. It is shown here that there exists a general class of systems that subsumes all these subclasses. This class is a generalization of the self-implicating structure. A characterization of this new class and an efficient diagnosis algorithm are found