Characterization of Diagnosabilities on the Bounded PMC Model

In this paper, we propose a new digragh model for system level fault diagnosis, which is called the $(f_1,f_{2})$-bounded Preparata–Metze–Chien (PMC) model (shortly, $(f_1,f_{2})$-BPMC). The $(f_1,f_{2})$-BPMC model projects a system such that the number of faulty processors that test faulty processors with the test results $0$ does not exceed $f_{2}$$(f_2\leq f_{1})$ provided that the upper bound on the number of faulty processors is $f_{1}$. This novel testing model compromisingly generalizes PMC model (Preparata, F.P., Metze, G. and Chien R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Tran. Electron. Comput.,EC-16, 848–854) and Barsi–Grandoni–Maestrini model (Barsi, F., Grandoni, F. and Maestrini, P. (1976) A theory of diagnosability of digital systems. IEEE Trans. Comput.C-25, 585–593). Then we present some characterizations for one-step diagnosibility under the $(f_1,f_{2})$-bounded PMC model, and determine the diagnosabilities of some special regular networks. Meanwhile, we establish the characterizations of $f_1/(n-1)$-diagnosability and three configurations of $f_1/(n-1)$-diagnosable system under the $(f_1,f_{2})$-BPMC model.

CORRECT DIAGNOSIS OF ALMOST ALL FAULTY UNITS IN A MULTIPROCESSOR SYSTEM

In a t/t-diagnosable system, all faulty units can be located to within a set of no more than t units as long as the number of faulty units present does not exceed t. Furthermore, a unique doubtful unit can be identified; in other words, all faulty units, except possibly for one, can be correctly identified in a t/t-diagnosable system. An open question is "Is t/t-diagnosability necessary for correctly identifying all but one faulty unit?" In this paper, we address the above question and provide an answer. We establish necessary and sufficient conditions for correct diagnosis of all except possibly one faulty unit. In addition, we show that the fault-free state is indistinguishable from a faulty state in a t/t-diagnosable system and propose a remedy. These considerations result in the definition and characterization of a new class of systems called t/-1 diagnosable systems.

DIAGNOSIS OF t/s-DIAGNOSABLE SYSTEMS

A t/s-diagnosable system permits diagnosis of faulty units within a set of s units provided the number of faulty units does not exceed t. A characterization of t/s-diagnosable systems is presented. This characterization is then used to develop an efficient algorithm for diagnosis of t/s-diagnosable systems. It is noted that a useful modification of the algorithm can be used for fault diagnosis of sequentially t-diagnosable systems.