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On sequential diagnosability of 2-dimensional meshes and tori

This paper considers sequential diagnosability of multiprocessor systems under the PMC model. In this model, the processors can test each other along communication links in the multiprocessor systems. A system is said to be sequentially t-diagnosable if at least one faulty processors can be identified from any set of test results provided that the number of faulty processors does not exceed t. The degree of sequential diagnosability of a multiprocessor system is maximum t such that the system is sequentially t-diagnosable. It is known that the degree of sequential diagnosability of the system modeled by a 2-dimensional square grid or torus with N vertices is Θ(N2/3). This paper generalizes this result, and is proved that that of a 2-dimentional l×m grid or torus is O(min{N2/3, √lN}), where N = l × m and l ≤ m.