In this paper, a t/(t+1)-diagnosable system is studied, which can locate a set S with |S|≤t+1 containing all faulty units only if the system has at most t faulty units. On the basis of the characterization of the t/(...In this paper, a t/(t+1)-diagnosable system is studied, which can locate a set S with |S|≤t+1 containing all faulty units only if the system has at most t faulty units. On the basis of the characterization of the t/(t+1)-diagnosable system, a necessary and sufficient condition is presented to judge whether a system is t/(t+1)-diagnosable. Meanwhile, this paper exposes some new and important properties of the t/(t+1)-diagnosable system to present the t/(t+1)-diagnosability of some networks. Furthermore, the following results for the t/(t+1)-diagnosability of some special networks are obtained: a hypercube network of n -dimensions is (3n-5)/(3n-4)-diagnosable, a star network of n -dimensions is (3n-5)/(3n-4)-diagnosable (n≥5) and a 2D-mesh (3D-mesh) with n 2(n 3) units is 8/9-diagnosable (11/12-diagnosable). This paper shows that in general, the t/(t+1)-diagnosability of a system is not only larger than its t/t -diagnosability , but also its classic diagnosability, specially the t/(t+1)-diagnosability of the hypercube network of n -dimensions is about 3 times as large as its classic t -diagnosability and about 1.5 times as large as its t/t -diagnosability.展开更多
Compared with accurate diagnosis, the system’s selfdiagnosing capability can be greatly increased through the t/kdiagnosis strategy at most k vertexes to be mistakenly identified as faulty under the comparison model,...Compared with accurate diagnosis, the system’s selfdiagnosing capability can be greatly increased through the t/kdiagnosis strategy at most k vertexes to be mistakenly identified as faulty under the comparison model, where k is typically a small number. Based on the Preparata, Metze, and Chien(PMC)model, the n-dimensional hypercube network is proved to be t/kdiagnosable. In this paper, based on the Maeng and Malek(MM)*model, a novel t/k-fault diagnosis(1≤k≤4) algorithm of ndimensional hypercube, called t/k-MM*-DIAG, is proposed to isolate all faulty processors within the set of nodes, among which the number of fault-free nodes identified wrongly as faulty is at most k. The time complexity in our algorithm is only O(2~n n~2).展开更多
A new diagnosis method, called Double-Syndrome diagnostic, is proposed, which can identify faulty nodes by comparing 2 different syndromes. For the same system, the average number of faulty nodes identified correctly ...A new diagnosis method, called Double-Syndrome diagnostic, is proposed, which can identify faulty nodes by comparing 2 different syndromes. For the same system, the average number of faulty nodes identified correctly by the Double-Syndrome diagnostic is much greater than the t-diagnosability and the(t_1/t_1)-diagnosability of the system. Furthermore, in order to identify the remaining faulty nodes in the system, two strategies of fault diagnostic are proposed, one is called(k, t)-fault diagnosable strategy, another is called(k, t/t)-fault diagnosable strategy. Besides, the conditional(k, t)-diagnosable((k, t/t)-diagnosable) system is introduced. Furthermore, the conditional diagnosabilities are proved for some regular(k, t)-diagnosable and(k, t/t)-diagnosable networks such as n-dimensional hypercube network and n-dimensional star network. And then, for a system, its(k,t)-conditional diagnosability and its(k, t/t)-conditional diagnosability are identical, and in the worst case, they are equal to their traditional conditional diagnosability.展开更多
基金Supported by the National Natural Science Foundation of China(No.61862003,61761006)the Natural Science Foundation of Guangxi of China(No.2018GXNSFDA281052)
文摘In this paper, a t/(t+1)-diagnosable system is studied, which can locate a set S with |S|≤t+1 containing all faulty units only if the system has at most t faulty units. On the basis of the characterization of the t/(t+1)-diagnosable system, a necessary and sufficient condition is presented to judge whether a system is t/(t+1)-diagnosable. Meanwhile, this paper exposes some new and important properties of the t/(t+1)-diagnosable system to present the t/(t+1)-diagnosability of some networks. Furthermore, the following results for the t/(t+1)-diagnosability of some special networks are obtained: a hypercube network of n -dimensions is (3n-5)/(3n-4)-diagnosable, a star network of n -dimensions is (3n-5)/(3n-4)-diagnosable (n≥5) and a 2D-mesh (3D-mesh) with n 2(n 3) units is 8/9-diagnosable (11/12-diagnosable). This paper shows that in general, the t/(t+1)-diagnosability of a system is not only larger than its t/t -diagnosability , but also its classic diagnosability, specially the t/(t+1)-diagnosability of the hypercube network of n -dimensions is about 3 times as large as its classic t -diagnosability and about 1.5 times as large as its t/t -diagnosability.
基金supported by the National Natural Science Foundation of China(61363002)
文摘Compared with accurate diagnosis, the system’s selfdiagnosing capability can be greatly increased through the t/kdiagnosis strategy at most k vertexes to be mistakenly identified as faulty under the comparison model, where k is typically a small number. Based on the Preparata, Metze, and Chien(PMC)model, the n-dimensional hypercube network is proved to be t/kdiagnosable. In this paper, based on the Maeng and Malek(MM)*model, a novel t/k-fault diagnosis(1≤k≤4) algorithm of ndimensional hypercube, called t/k-MM*-DIAG, is proposed to isolate all faulty processors within the set of nodes, among which the number of fault-free nodes identified wrongly as faulty is at most k. The time complexity in our algorithm is only O(2~n n~2).
基金Supported by the National Natural Science Foundation of China(No.61862003,61761006)the Natural Science Foundation of Guangxi of China(No.2018GXNSFDA281052,2017GXNSFAA198263)。
文摘A new diagnosis method, called Double-Syndrome diagnostic, is proposed, which can identify faulty nodes by comparing 2 different syndromes. For the same system, the average number of faulty nodes identified correctly by the Double-Syndrome diagnostic is much greater than the t-diagnosability and the(t_1/t_1)-diagnosability of the system. Furthermore, in order to identify the remaining faulty nodes in the system, two strategies of fault diagnostic are proposed, one is called(k, t)-fault diagnosable strategy, another is called(k, t/t)-fault diagnosable strategy. Besides, the conditional(k, t)-diagnosable((k, t/t)-diagnosable) system is introduced. Furthermore, the conditional diagnosabilities are proved for some regular(k, t)-diagnosable and(k, t/t)-diagnosable networks such as n-dimensional hypercube network and n-dimensional star network. And then, for a system, its(k,t)-conditional diagnosability and its(k, t/t)-conditional diagnosability are identical, and in the worst case, they are equal to their traditional conditional diagnosability.
基金Supported by the National Natural Sciences Foundation of China (No. 61064002)the Program for New Century Excellent Talents in University China (No. Degrte NCET-06-0756)
文摘In this paper, the concepts of （α,β） vague mappings, surjective （α,β） vague mappings, injective （α,β） vague mappings, bijective （α,β） vague mappings, （α,β） adjoin vague mappings, （α,β） vague monomorphism, （α,β） vague epimorphism, （α,β） vague isomorphism, （α,β） Vague par-tition are introduced through the so-called （α,β） hierarchical divide vague relations We extend the results on fuzzy mappings, and obtain some of their properties.
