We examine diagnosis of processor array systems formed as two-dimensional grids, 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. We establish an upper bound on the maximum number of faults that can be sustained without invalidating the test results under worst case conditions. We give test schedules and diagnostic algorithms that 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.

This paper proposes new algorithms for diagnosing (detection, identification and location) baseline multistage interconnection networks (MIN) as one of the basic units in a massively parallel system. This is accomplished in the presence of single and multiple faults under a new fault model. This model referred to as the geometric fault model, considers defective crossing connections which are located between adjacent stages, internally to the MIN (therefore, a fault corresponds to a physical bridge fault between two connections). It is shown that this type of fault affects the correct geometry of the network, thus requiring a different testing approach than previous methods. Initially, an algorithm which detects the presence of bridge faults (both in the single and multiple fault cases), is presented. For a single bridge fault, the proposed algorithm locates the fault except in an unique pathological case under which it is logically impossible to differentiate between two equivalent locations of the fault (however, the switching element affected by this fault is uniquely located). The proposed algorithm requires log2 N test vectors to diagnose the MIN as fault free (where N is the number of input lines to the MIN). For fully diagnosing a single bridge fault, this algorithm requires at most 2 log2 N tests and terminates when multiple bridge faults are detected. Subsequently, an algorithm which locates all bridge faults is given. The number of required test vectors is O(N). Fault location of each bridge fault is accomplished in terms of the two lines in the bridge and the numbers of the stages between which it occurs. Illustrative examples are given.