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

It is known that among the diagnosable systems modeled as in PMC model, there exist several subclasses of systems that can be diagnosed more efficiently than the general case. Some of these subclasses are D(n, t, X) systems, self-implicating systems, systems having connection assignment digraph of node connectivity t and so on. It has been shown in the literature that some of these classes are unrelated. An obvious question is: does there exist any class of systems that subsumes all these subclasses? In this paper, we have found an affirmative answer to this question. We present a generalization of the self-implicating structure and show that this generalized class subsumes all these subclasses. We find a characterization of this new class and find an efficient diagnosis algorithm.