Covering Arrays for Equivalence Classes of Words

Abstract

Covering arrays for words of length $t$ over a $d$ letter alphabet are $k\times n$ arrays with entries from the alphabet so that for each choice of $t$ columns, each of the $d^t$ $t$-letter words appears at least once among the rows of the selected columns. We study two schemes in which all words are not considered to be different. In the first case words are equivalent if they induce the same partition of a $t$ element set. In the second case, words of the same weight are equivalent. In both cases we produce logarithmic upper bounds on the minimum size $k=k(n)$ of a covering array. Definitive results for $t=2,3,4$, as well as general results, are provided.

17 pages

References in corpus (2)

• Covering Array Bounds Using Analytical Techniques
• $t$-Covering Arrays Generated by a Tiling Probability Model