Search

We examine the diagnosis of processor array systems formed as two-dimensional arrays, with boundaries, and either four or eight neighbors for each interior processor. We employ a parallel test schedule. Neighboring processors test each other, and report the results. Our diagnostic objective is to find a fault-free processor or set of processors. The system may then be sequentially diagnosed by repairing those processors tested faulty according to the identified fault-free set, or a job may be run on the identified fault-free processors. We establish an upper bound on the maximum number of faults which can be sustained without invalidating the test results under worst case conditions. We give test schedules and diagnostic algorithms which meet the upper bound as far as the highest order term. We compare these near optimal diagnostic algorithms to alternative algorithms, both new and already in the literature, and against an upper bound ideal case algorithm, which is not necessarily practically realizable. For eight-way array systems with N processors, an ideal algorithm has diagnosability 3N/sup 2/3/-2N/sup 1/2/ plus lower-order terms. No algorithm exists which can exceed this. We give an algorithm which starts with tests on diagonally connected processors, and which achieves approximately this diagnosability. So the given algorithm is optimal to within the two most significant terms of the maximum diagnosability. Similarly, for four-way array systems with N processors, no algorithm can have diagnosability exceeding 3N/sup 2/3//2/sup 1/3/-2N/sup 1/2/ plus lower-order terms. And we give an algorithm which begins with tests arranged in a zigzag pattern, one consisting of pairing nodes for tests in two different directions in two consecutive test stages; this algorithm achieves diagnosability (3/2)(5/2)/sup 1/3/N/sup 2/3/-(5/4)N/sup 1/2/ plus lower-order terms, which is about 0.85 of the upper bound due to an ideal algorithm.

This paper presents an approach for the maximal diagnosis of all faults (stuck-at, open and short) in the interconnect of a random access memory (RAM); and the interconnect includes data and address lines. This approach accomplishes maximal diagnosis under a complex model in which the lines in the interconnect of the RAM can be affected by multiple faults. Maximal diagnosis consists of detection and location of all diagnosable faults as well as type identification of multiple faults affecting each line. The proposed algorithm (referred to as the Improved Maximal Diagnosis Algorithm, or IMDA) requires max{n,m-1}+n+3 WRITE and max{n,m}+2n READ, where n is the number of address lines and m is the number of data lines. IMDA executes in three different steps: the first step diagnoses the data lines (and in particular the stuck-at faults); the second step accomplishes maximal diagnosis of the shorts (involving either the data lines only, or the data and address lines); and the third step completes the diagnosis of the address lines.