(t, k)-Diagnosable System: A Generalization of the PMC Models Toru Araki, Member, IEEE Computer Society, and

Abstract—In this paper, we introduce a new model for diagnosable systems called t; k-diagnosable system which guarantees that at least k faulty units (processors) in a system are detected provided that the number of faulty units does not exceed t. This system includes classical one-step diagnosable systems and sequentially diagnosable systems. We prove a necessary and sufficient condition for \u85t; k-diagnosable system, and discuss a lower bound for diagnosability. Finally, we deal with a relation between \u85t; k-diagnosability and diagnosability of classical basic models. Index Terms—Fault diagnosis, PMC model, one-step t-diagnosis, sequential t-diagnosis, diagnosability, Cartesian product