Correct diagnosis of almost all faulty units in a multiprocessor system

In a t/t-diagnosable system all faulty units can be located to within a set of no more than t units as long as the number of faulty units present does not exceed t. Furthermore, a unique doubtful unit can be identified; in other words, all faulty units, except possibly for one, can be correctly identified in a t/t-diagnosable system. An open question is “is t/t-diagnosability necessary for correctly identifying all but one faulty unit?” In this paper we address the above question and provide an answer. We establish necessary and sufficient conditions for correct diagnosis of all except possibly one faulty unit. In addition, we show that the faulty-free state is indistinguishable from a faulty state in a t/t-diagnosable system and propose a remedy. These considerations result in the definition and characterization of a new class of systems called t/-l diagnosable systems