Extra Conditional Diagnosability of Hypercubes under the Bounded PMC Model

Abstract

The h-extra conditional diagnosability is different from the traditional diagnosability, which restricts that each component has no fewer than $h+1$ processors after the deletion of the faulty sets in the system. The $(f_{1}, f_{2})$ -BPMC model is a combination of the PMC model and BGM model, assuming that the upper bound number of failed processors is $f_{1}$ and no more than $f_{2}$ failed processors that can evaluate a faulty processor as non-faulty. In this paper, inspired by the $(f_{1}, f_{2})$ - BPMC model, we propose a diagnosis model called $f$ -BPMC model by relaxing the restriction of $f_{1}$. In this model, it only assumes that at most $f$ failed processors for a given system that can evaluate faulty processors as non-faulty. We then study the h-extra conditional diagnosability of interconnection networks under the $f$ -BPMC model and explore some of its properties. Finally, the h-extra conditional diagnosability is applied to hypercubes under the $f$ -BPMC model.