On fault identification in interconnection networks under the comparison model (Q1727214)

Summary: We propose three characterization theorems of \(t / t\)-diagnosable systems under the comparison model. By these characterization theorems we present some properties of \(t / t\)-diagnosable systems. Furthermore, for a given network system, we introduce a new method to determine a range from \(t_{\mathrm{min}}\) to \(t_{\mathrm{max}}\) conveniently, in which the system is at least \(t_{\mathrm{min}} / t_{\mathrm{min}}\)-diagnosable and at most \(t_{\mathrm{max}} / t_{\mathrm{max}}\)-diagnosable. By applying our results to some well-known networks such as \(n\)-dimensional hypercube, \(2 D\) (\(3 D\)) mesh, and permutation star graph, we figure out their \(t / t\)-diagnosability.