Binary Covering Arrays and Existentially Closed Graphs

Existentially closed central extensions of locally finite p-groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100066093 ◽

1986 ◽

Vol 100 (2) ◽

pp. 281-301 ◽

Cited By ~ 5

Author(s):

Felix Leinen ◽

Richard E. Phillips

Keyword(s):

Central Extensions ◽

Locally Finite ◽

Existentially Closed ◽

Image Position

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

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Factorials Experiments, Covering Arrays, and Combinatorial Testing

Mathematics in Computer Science ◽

10.1007/s11786-021-00502-7 ◽

2021 ◽

Author(s):

Raghu N. Kacker ◽

D. Richard Kuhn ◽

Yu Lei ◽

Dimitris E. Simos

Keyword(s):

Combinatorial Testing ◽

Covering Arrays

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Finitely generic models of TUH, for certain model companionable theories T

Journal of Symbolic Logic ◽

10.2307/2274316 ◽

1985 ◽

Vol 50 (3) ◽

pp. 604-610

Author(s):

Francoise Point

Keyword(s):

Discriminator Variety ◽

Generic Models ◽

Elementary Class ◽

Ordered Groups ◽

Existentially Closed ◽

Closed Element ◽

Starting Point ◽

Joint Embedding ◽

Joint Embedding Property ◽

Generic Elements

The starting point of this work was Saracino and Wood's description of the finitely generic abelian ordered groups [S-W].We generalize the result of Saracino and Wood to a class ∑UH of subdirect products of substructures of elements of a class ∑, which has some relationships with the discriminator variety V(∑t) generated by ∑. More precisely, let ∑ be an elementary class of L-algebras with theory T. Burris and Werner have shown that if ∑ has a model companion then the existentially closed models in the discriminator variety V(∑t) form an elementary class which they have axiomatized. In general it is not the case that the existentially closed elements of ∑UH form an elementary class. For instance, take for ∑ the class ∑0 of linearly ordered abelian groups (see [G-P]).We determine the finitely generic elements of ∑UH via the three following conditions on T:(1) There is an open L-formula which says in any element of ∑UH that the complement of equalizers do not overlap.(2) There is an existentially closed element of ∑UH which is an L-reduct of an element of V(∑t) and whose L-extensions respect the relationships between the complements of the equalizers.(3) For any models A, B of T, there exists a model C of TUH such that A and B embed in C.(Condition (3) is weaker then “T has the joint embedding property”. It is satisfied for example if every model of T has a one-element substructure. Condition (3) implies that ∑UH has the joint embedding property and therefore that the class of finitely generic elements of ∑UH is complete.)

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New optimal covering arrays using an orderly algorithm

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500118 ◽

2018 ◽

Vol 10 (01) ◽

pp. 1850011 ◽

Cited By ~ 1

Author(s):

Idelfonso Izquierdo-Marquez ◽

Jose Torres-Jimenez

Keyword(s):

Small Subset ◽

Computational Results ◽

Covering Array ◽

Covering Arrays ◽

Computational Search ◽

Minimum Number ◽

Orderly Algorithm

A covering array [Formula: see text] is an [Formula: see text] array such that every [Formula: see text] subarray covers at least once each [Formula: see text]-tuple from [Formula: see text] symbols. For given [Formula: see text], [Formula: see text], and [Formula: see text], the minimum number of rows for which exists a CA is denoted by [Formula: see text] (CAN stands for Covering Array Number) and the corresponding CA is optimal. Optimal covering arrays have been determined algebraically for a small subset of cases; but another alternative to find CANs is the use of computational search. The present work introduces a new orderly algorithm to construct non-isomorphic covering arrays; this algorithm is an improvement of a previously reported algorithm for the same purpose. The construction of non-isomorphic covering arrays is used to prove the nonexistence of certain covering arrays whose nonexistence implies the optimality of other covering arrays. From the computational results obtained, the following CANs were established: [Formula: see text] for [Formula: see text], [Formula: see text], and [Formula: see text]. In addition, the new result [Formula: see text], and the already known existence of [Formula: see text], imply [Formula: see text].

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Refining the In-Parameter-Order Strategy for Constructing Covering Arrays

Journal of Research of the National Institute of Standards and Technology ◽

10.6028/jres.113.022 ◽

2008 ◽

Vol 113 (5) ◽

pp. 287 ◽

Cited By ~ 102

Author(s):

Michael Forbes ◽

Jim Lawrence ◽

Yu Lei ◽

Raghu N. Kacker ◽

D. Richard Kuhn

Keyword(s):

Covering Arrays

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Research Notes: Binary Test-Suites Using Covering Arrays

International Journal of Software Engineering and Knowledge Engineering ◽

10.1142/s0218194018500377 ◽

2018 ◽

Vol 28 (09) ◽

pp. 1321-1337 ◽

Cited By ~ 1

Author(s):

Jose Torres-Jimenez ◽

Himer Avila-George ◽

Ezra Federico Parra-González

Keyword(s):

Software Testing ◽

Test Generation ◽

Software Systems ◽

Combinatorial Testing ◽

Covering Array ◽

Covering Arrays ◽

Almost All ◽

Generation Problem ◽

Test Suites

Software testing is an essential activity to ensure the quality of software systems. Combinatorial testing is a method that facilitates the software testing process; it is based on an empirical evidence where almost all faults in a software component are due to the interaction of very few parameters. The test generation problem for combinatorial testing can be represented as the construction of a matrix that has certain properties; typically this matrix is a covering array. Covering arrays have a small number of tests, in comparison with an exhaustive approach, and provide a level of interaction coverage among the parameters involved. This paper presents a repository that contains binary covering arrays involving many levels of interaction. Also, it discusses the importance of covering array repositories in the construction of better covering arrays. In most of the cases, the size of the covering arrays included in the repository reported here are the best upper bounds known, moreover, the files containing the matrices of these covering arrays are available to be downloaded. The final purpose of our Binary Covering Arrays Repository (BCAR) is to provide software testing practitioners the best-known binary test-suites.

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