(t, k)-Diagnosable System: A Generalization of the PMC Models
IEEE Transactions on Computers
Diagnosabilities of Regular Networks
IEEE Transactions on Parallel and Distributed Systems
Diagnosability of Two-Matching Composition Networks
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Conditional diagnosability of matching composition networks under the PMC model
IEEE Transactions on Circuits and Systems II: Express Briefs
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Conditional diagnosability of matching composition networks under the MM* model
Information Sciences: an International Journal
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A classic PMC (Preparata, Metze, and Chien) multiprocessor system [F. P. Preparata, G. Metze, and R. T. Chien, IEEE Trans. Electr. Comput., EC-16 (1967), pp. 848--854] composed of $n$ units is said to be $t/(t+1)$ diagnosable [A. D. Friedman, A new measure of digital system diagnosis, in Dig. 1975 Int. Symp. Fault-Tolerant Comput., 1975, pp. 167--170] if, given a syndrome (complete collection of test results), the set of faulty units can be isolated to within a set of at most $t+1$ units, assuming that at most $t$ units in the system are faulty. This paper presents a methodology for determining when a unit $v$ can belong to an allowable fault set of cardinality at most $t$. Based on this methodology, for a given syndrome in a $t/(t+1)$-diagnosable system, the authors establish a necessary and sufficient condition for a vertex $v$ to belong to an allowable fault set of cardinality at most $t$ and certain properties of $t/(t+1)$-diagnosable systems. This condition leads to an $O(n^{3.5}) t/(t+1)$-diagnosis algorithm. This $t/(t+1)$-diagnosis algorithm complements the $t/(t+1)$-diagnosability algorithm of Sullivan [The complexity of system-level fault diagnosis and diagnosability, Ph. D. thesis, Yale University, New Haven, CT, 1986].