Abstract: Fault diagnosis plays a very important role in maintaining the reliability of multiprocessor systems,and the diagno-sability is an important measure of the diagnosis capability of the system.Except for the traditional diagnosability,there are also conditional diagnosability,such as g-good-neighbor conditional diagnosability,g-extra conditional diagnosability,etc.Where g-good-neighbor conditional diagnosability is defined under the condition that every fault-free vertex has at least g fault-free neighbors,and g-extra conditional diagnosability is defined under the condition that every fault-free component contains more than g vertices.Fault diagnosis needs to be performed under a specific diagnosis model,such as PMC model,symmetric PMC model,in which the symmetric PMC model is a new diagnosis model proposed by adding two assumptions to the PMC model.The n-dimensional hypercube has many excellent properties,so it has been widely studied by researchers.At present,there are a number of diagnosability studies under the PMC models,but there is a lack of diagnosability studies under the symmetric PMC models.This paper first investigates the upper and lower bounds for the g-good-neighbor conditional diagnosability of hypercubes under the symmetric PMC model,with an upper bound of 2^g+1(n－g－1)+2^g－1 when n≥4 and 0≤g≤n－4 and a lower bound of (2n－2^g+1+1)2^g－1+(n－g)2^g－1－1 when g≥0 and n≥max{g+4,2^g+1－2^－g－g－1}.Also study the upper and lower bounds for the g-extra conditional diagnosability of hypercubes under the symmetric PMC model,the upper bound is 2n(g+1)－5g－2C²_g－2 when n≥4 and 0≤g≤n－4,and the lower bound is$\frac{3}{2} n(g+1)-g-\frac{5}{2} C_{g+1}^{2}-1$ when n≥4 and $0 \leqslant g \leqslant \min \left\{n-4,\left\lfloor\frac{2}{3} n\right\rfloor\right\}$.Finally,the correctness of the relevant theoretical conclusions is verified by simulation experiments.

Key words: Interconnection network, Hypercube, System level diagnosis, Symmetric PMC model, Conditional diagnosability