(t, k)-diagnosable system: a generalization of the PMC models

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 (t, k)-diagnosable system, and discuss a lower bound for diagnosability. Finally, we deal with a relation between (t, k)-diagnosability and diagnosability of classical basic models.