Disjoint Covers in Replicated Heterogeneous Arrays

Reconfigurable chips are fabricated with redundant elements that can be used to replace the faulty elements. The fault cover problem consists of finding an assignment of redundant elements to the faulty elements such that all of the faults are repaired. In reconfigurable chips that consist of arrays of elements, redundant elements are configured as spare rows and spare columns. This paper considers the problem in which a chip contains several replicates of a heterogeneous array, one or more sets of spare rows, and one or more sets of spare columns. Each set of spare rows is identical to the set of rows in the array, and each set of spare columns is identical to the set of columns in the array. Specifically, an ith spare row can only be used to replace an ith row of an array, and similarly with spare columns. Repairing the chip reduces to finding a cover for the faults in each of the arrays. These covers must be disjoint; that is, a particular spare row or spare column can be used in the cover of at most one array. Results are presented for three fault cover problems that arise under these conditions