Conditional Diagnosability Of The EQ_n,k And Q（d₁,d₂）under The PMC Model

There are many ways for computer to process large-scale data. Along with the popularization of the Internet and high-speed development of cloud computing, network and computer have closely combined together. There are large number of processes and servers distributed in the network, so they breakdown or make a fault are inevitable. How can the system judge faults without adding investment and consumption by itself is very practical significance.Using undirected graph theory analysis is the common method to analyse the network system. Let the processes be the nodes of graph, and let the links be the edges of graph. We can construct the abstract graph of system. If there are some processes or servers doesn’t work, using a certain algorithm to find the error nodes is defined as conditional diagnosability. This type of algorithm has been researched in-depth. They can applied to complex network system and multi-processer system.The research for some special network topology is more mature. For example, Qn has been applied to IBM machine. EOn.k and Q(d1,d2,...,dn) are the improvement and promotion of Qn. Not only inherited the advantage of On, they two also greatly improved the function of network. Using the exhaustive method to program on the small-scale system, we firstly find the law and then strictly prove it by mathematical method. We get the following conclusions:(1) In the case of n≥3, k≥3, the conditional diagnosability of EOn.k is4n-3。(2) In the case of n≥3,k=2, the conditional diagnosability of EQn.k is4n-7。(3) In the case of d2≤2d1,t。(O(d1,d2))=2d1+2d2-7。(4) In the case of d2≥2d1+1, t。(O(d1,d2))=3d,+d2-7.