Compressing inconsistent data

Körner, János; Lucertini, M.

doi:10.1109/18.335882

Cited by 28 publications

(22 citation statements)

References 47 publications

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“…Applications of these covering arrays and related structures to circuit testing, digital communication, network design, etc., are discussed in [4], [8], [12], [15], [19], [44], [51], [52], [54], [55]. The survey article by Korner and Lucertini [35] gives an overview of these and several related problems. Honkala [28] uses t-covering arrays in the construction of codes with small covering radius.…”

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confidence: 99%

Covering arrays and intersecting codes

Sloane

1993

J of Combinatorial Designs

137

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A t-covering array is a set of k binary vectors of length n with the property that, in any t coordinate positions, all 2t possibilities occur at least once. Such arrays are used for example in circuit testing, and one wishes to minimize k for given values of n and t. The case t = 2 was solved by Rknyi, Katona, and Kleitman and Spencer. The present article is concerned with the case t = 3, where important (but unpublished) contributions were made by Busschbach and Roux in the 1980s. One of the principal constructions makes use of intersecting codes (linear codes with the property that any two nonzero codewords meet). This article studies the properties of 3-covering arrays and intersecting codes, and gives a table of the best 3-covering arrays presently known. For large n the minimal k satisfies 3.21256 < k / log n < 7.56444. 01993

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confidence: 99%

Covering arrays and intersecting codes

Sloane

1993

J of Combinatorial Designs

137

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“…Many of the early results were established using this vernacular, but we for the most part translate to the language of covering arrays. Poljak, Pultr, and Rödl [58] and Körner and Lucertini [44] discuss combinatorial problems related to qualitative independence.…”

Section: Covering Arraysmentioning

confidence: 99%

Locating and detecting arrays for interaction faults

2007

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The identification of interaction faults in component-based systems has focussed on indicating the presence of faults, rather than their location and magnitude. While this is a valuable step in screening a system for interaction faults prior to its release, it provides little information to assist in the correction of such faults. Consequently tests to reveal the location of interaction faults are of interest. The problem of nonadaptive location of interaction faults is formalized under the hypothesis that the system contains (at most) some number d of faults, each involving (at most) some number t of interacting factors. Restrictions on the number and size of the putative faults lead to numerous variants of the basic problem. The relationships between this class of problems and interaction testing using covering arrays to indicate the presence of faults, designed experiments to measure and model faults, and combinatorial group testing to locate faults in a more general testing scenario, are all examined. While each has some definite similarities with the fault location problems for componentbased systems, each has some striking differences as well. In this paper, we formulate the combinatorial problems for locating and detecting arrays to undertake interaction fault location. Necessary conditions for existence are established, and using a close connection to covering arrays, asymptotic bounds on the size of minimal locating and detecting arrays are established.

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“…The determination of CAN(t, k, v) has been the subject of much research (see, for example, [3,5,6,8,10,11,17]). In literature, a CA(N ; t, k, v) was also studied under various equivalent objects such as a transversal covering [20], a t-surjective array [19] and a t-qualitatively independent partition of a set of size N [15,18].…”

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Covering arrays of strength 3 and 4 from holey difference matrices

Yin

2008

Des. Codes Cryptogr.

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A covering array CA(N ; t, k, v) is an N × k array with entries from a set X of v symbols such that every N × t sub-array contains all t-tuples over X at least once, where t is the strength of the array. The minimum size N for which a CA(N ; t, k, v) exists is called the covering array number and denoted by CAN(t, k, v). Covering arrays are used in experiments to screen for interactions among t-subsets of k components. One of the main problems on covering arrays is to construct a CA(N ; t, k, v) for given parameters (t, k, v) so that N is as small as possible. In this paper, we present some constructions of covering arrays of strengths 3 and 4 via holey difference matrices with prescribed properties. As a consequence, some of known bounds on covering array number are improved. In particular, it is proved that (1) CAN(3, 5, 2v) ≤ 2v 2 (4v + 1) for any odd positive integer v with gcd(v, 9) = 3; (2) CAN

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Compressing inconsistent data

Cited by 28 publications

References 47 publications

Covering arrays and intersecting codes

Covering arrays and intersecting codes

Locating and detecting arrays for interaction faults

Covering arrays of strength 3 and 4 from holey difference matrices

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