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
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.
