t/t-Diagnosability of regular graphs under the PMC model
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Conditional diagnosability of matching composition networks under the MM* model
Information Sciences: an International Journal
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($t$, $k$)-diagnosis, which is a generalization of sequential diagnosis, requires at least $k$ faulty processors identified and replaced (or repaired) in each iteration provided there are at most $t$ faulty processors, where $t \ge k$. This paper suggests lower bounds on the degrees of $(t,k)$-diagnosability of multiprocessor systems under both the PMC and the MM* models. As a consequence, grids and tori of $d$ dimensions are shown to be $(\Omega(N^\frac{d}{d+1})$, $\Omega(d))$-diagnosable and $(\Omega(N^\frac{d}{d+1})$, $\Omega(2d))$-diagnosable, respectively, where $N$ is the number of processors.