17,244 research outputs found
Covering Arrays for Equivalence Classes of Words
Covering arrays for words of length t over a d letter alphabet are k × n arrays with entries from the alphabet so that for each choice of t columns, each of the dt 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 weighted sum are equivalent. In both cases we produce logarithmic upper bounds on the minimum size k = k(n) of a covering array. Most definitive results are for t = 2, 3, 4
Covering Arrays for Equivalence Classes of Words
Covering arrays for words of length over a letter alphabet are arrays with entries from the alphabet so that for each choice of
columns, each of the -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 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 of a covering array. Definitive results for
, as well as general results, are provided.Comment: 17 page
Covering Arrays and Fault Detection
Given their several applications, covering arrays have become a topic of significance over the last twenty years in both the mathematical and computer science fields. A covering array is a N × k array with strength t, k rows of length N, entries from the set {0, 1, ..., v − 1}, and all vt possible combinations occur between any t columns, where N,k,t, and v are positive integers. The focus of our research was to explore the different constructions of strength two and strength three covering arrays, to find better covering arrays (i.e. more cost and time efficient covering arrays), and to see if covering arrays can detect a fault in a system. Through analyzing the covering arrays that we constructed, we were able to successfully prove that in general, a covering array of strength k + 1 can detect a single fault between any k or fewer variables in a system. Some areas of future research would include finding the location of a fault in a system or detecting two or more faults in a system
Partial Covering Arrays: Algorithms and Asymptotics
A covering array is an array with entries
in , for which every subarray contains each
-tuple of among its rows. Covering arrays find
application in interaction testing, including software and hardware testing,
advanced materials development, and biological systems. A central question is
to determine or bound , the minimum number of rows of
a . The well known bound
is not too far from being
asymptotically optimal. Sensible relaxations of the covering requirement arise
when (1) the set need only be contained among the rows
of at least of the subarrays and (2) the
rows of every subarray need only contain a (large) subset of . In this paper, using probabilistic methods, significant
improvements on the covering array upper bound are established for both
relaxations, and for the conjunction of the two. In each case, a randomized
algorithm constructs such arrays in expected polynomial time
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