Upper bounds for the degree of sequential diagnosability

It is known that an n-dimensional grid with N vertices, an N-vertex hypercube, and a k-ary tree with N vertices are sequentially /spl Omega/(N/sup n/(n+1)/)-, /spl Omega/(N log log N/log N)-, and /spl Omega/(/spl radic/N/k)-diagnosable, respectively. This paper shows that they are sequentially O(N/sup n/(n+1)/)-, O(N log log N//spl radic/log N)-, and o(/spl radic/kN)-diagnosable, respectively.