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 se t of no more than t units as long as the number of faulty units present doe s not exceed t. Furthermore, a unique doubtful unit can be identified; in o ther words, all faulty units, except possibly for one, can be correctly ide ntified in a tit-diagnosable system. An open question is "Is t/t-diagnosabi lity necessary for correctly identifying all but one faulty unit?" In this paper, we address the above question and provide an answer. We establish ne cessary and sufficient conditions for correct diagnosis of all except possi bly one faulty unit. In addition, we show that the fault-free state is indi stinguishable 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/ - 1 diagnosable systems.