Mixed covering arrays of strength three with few factors

Variable strength orthogonal array, as a special form of variable strength covering array, plays an important role in computer software testing and cryptography. In this paper, we study the construction of variable strength orthogonal arrays with strength two containing strength greater than two by Galois field and construct some variable strength orthogonal arrays with strength l containing strength greater than l by Fanconstruction.

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“…By assumption, we know that an OA(u, w k 3. From Lemma 7, an OA(16 4 , 16 17 , 4) exists. Hence, a 16-divisible OA(16 4 , 16 16 , 4) exists.…”

Section: Construction Of Voas By Fan-constructionmentioning

confidence: 93%

“…Soon covering arrays (CAs) the natural generalizations of OAs are introduced in software testing. Motivated by the effectiveness of CAs, a number of recent studies have focused on the construction of CAs [9]- [17].…”

Section: Introductionmentioning

confidence: 99%

On the Construction of Variable Strength Orthogonal Arrays

ZHANG

Pang

2023

IEICE Trans. Fundamentals

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“…Now, suppose that e ≥ 1. Insert a column vector ( j, j, • • • , j) of length N 2 to the front of the ith column of B to form an N 2 ×k array B j , where j [14]. By Lemma 2.1, we only need to prove that M is a (1, t)-LA, i.e., ρ(M, T 1 ) ρ(M, T 2 ) for any two distinct t-way interactions T 1 and T 2 , where T 1 = {(a 1 , u a 1 ), • • • , (a t , u a t )} and…”

Section: Methods For Constructingmentioning

confidence: 99%

“…However, in real life, different factors have different numbers of possible values. Thus, mixed-level CAs or mixed covering arrays (MCAs) are a natural extension of covering array research, which improves their suitability for applications [2,3,11,14,26,31]. A CA or MCA as a test suite can be used to detect the presence of failure-triggered interactions.…”

Section: Introductionmentioning

confidence: 99%

Locating arrays with mixed alphabet sizes

Shi,

Jin,

Tsuchiya

2020

Preprint

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Locating arrays (LAs) can be used to detect and identify interaction faults among factors in a component-based system. The optimality and constructions of LAs with a single fault have been investigated extensively under the assumption that all the factors have the same values. However, in real life, different factors in a system have different numbers of possible values. Thus, it is necessary for LAs to satisfy such requirements. We herein establish a general lower bound on the size of mixed-level ( 1, t)-locating arrays. Some methods for constructing LAs including direct and recursive constructions are provided. In particular, constructions that produce optimal LAs satisfying the lower bound are described. Additionally, some series of optimal LAs satisfying the lower bound are presented.

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“…The rows represent tests to be performed, in which a value for each factor is dictated. Covering arrays have been extensively studied; see Colbourn (2004) for a survey for CAs, and Colbourn et al (2006), Moura et al (2003) and Colbourn et al (2011) for their properties, applications and efficient constructions.…”

Section: Introductionmentioning

confidence: 99%

Optimum mixed level detecting arrays

Shi¹,

Tang²,

Yin³

2014

Ann. Statist.

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As a type of search design, a detecting array can be used to generate test suites to identify and detect faults caused by interactions of factors in a component-based system. Recently, the construction and optimality of detecting arrays have been investigated in depth in the case where all the factors are assumed to have the same number of levels. However, for real world applications, it is more desirable to use detecting arrays in which the various factors may have different numbers of levels. This paper gives a general criterion to measure the optimality of a mixed level detecting array in terms of its size. Based on this optimality criterion, the combinatorial characteristics of mixed level detecting arrays of optimum size are investigated. This enables us to construct optimum mixed level detecting arrays with a heuristic optimization algorithm and combinatorial methods. As a result, some existence results for optimum mixed level detecting arrays achieving a lower bound are provided for practical use.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1228 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Mixed covering arrays of strength three with few factors

Cited by 6 publications

References 20 publications

On the Construction of Variable Strength Orthogonal Arrays

On the Construction of Variable Strength Orthogonal Arrays

Locating arrays with mixed alphabet sizes

Optimum mixed level detecting arrays

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