Rg conditional diagnosability: A novel generalized measure of system-level diagnosis

Abstract

System-level diagnosis has become an important diagnosis method for multiprocessor systems. Among all system-level diagnosis measures, diagnosability is relatively small. The conditional diagnosability constraint that each vertex has at least one good neighbor is relatively conservative when the dimension is far greater than 1, and g-good-neighbor conditional diagnosability does not consider this restriction on faulty vertices. Therefore, a thorough study of diagnosability under the condition that each vertex has at least g good neighbors is an appealing subject. Motivated by Rg vertex connectivity, in this paper, we introduce a novel generalized system-level diagnosis measure named Rg conditional diagnosability, which assumes that every processor has at least g good neighbors. The popular conditional diagnosability is a special case of Rg conditional diagnosability when g=1. Then, we determine that the Rg conditional diagnosability of n-dimensional hypercube Qn under the Preparata Metze Chien (PMC) model is 22g(n−2g)+22g−1−1.