The diagnosability of thek-aryn-cubes using the pessimistic strategy

The pessimistic strategy, also called the t 1/t 1-diagnosis strategy, allows to contain all faulty vertices and at most one fault-free vertex. However, the degree of the diagnosability of a system increases quickly using the pessimistic strategy. In this paper, we consider the k-ary n-cube, which is an important hypercube variant, and show that the 3-ary n-cube and k-ary n-cube with k≥4 are (4n−3)/(4n−3)-diagnosable and (4n−2)/(4n−2)-diagnosable, respectively. Finally, we obtain the degree of the diagnosability of the tori using the pessimistic strategy.