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detecting arrays and Their Optimality

Acta Mathematica Sinica,English Series 2011年第12期27卷 2309-2318页

作者： Yu TANG Jian Xing YIN Department of Mathematics Soochow University Suzhou 215006 P. R. China

detecting arrays were proposed by Colbourn and McClary in 2008, which are of interest in generating software test suites to cover all t-sets of component interactions and detect interaction faults in component-based systems. So far, optimality and constructions of detecting arrays have not been studied systematically. Indeed, no useful benchmark to measure the optimality of detecting arrays has previously been given, and only some sporadic examples of optimal detecting arrays have been found. This paper tries to take the first step by presenting a lower bound on the size of detecting arrays and some methods of constructing optimal detecting arrays. A number of infinite series of optimal detecting arrays are then obtained.

关键词： detecting arrays interaction faults bounds optimality constructions

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Optimum detecting arrays for Independent Interaction Faults

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Acta Mathematica Sinica,English Series 2016年第2期32卷 199-212页

作者： Ce SHI Cheng Min WANG School of Mathematics and Information Science Shanghai Lixin University of Commerce School of Science Jiangnan University

The use of detecting arrays （DTAs） is motivated by the need to locate and detect interaction faults arising between the factors in a component-based system in software testing. The optimality and construction of DTAs have been investigated in depth for the case in which all the interaction faults are assumed to have the same strength; however, as a practical concern, the strengths of these faults are not always identical. For real world applications, it would be desirable for a DTA to be able to identify and detect faulty interactions of a strength equal to or less than a specified value under the assumption that the faulty interactions are independent from one another. To the best of our knowledge, the optimality and construction of DTAs for independent interaction faults have not been studied systematically before, In this paper, we establish a general lower bound on the size of DTAs for independent interaction faults and explore the combinatorial feature that enable these DTAs to meet the lower bound. Taking advantage of this combinatorial characterization, several classes of optimum DTAs meeting the lower bound are presented.

关键词： detecting arrays super-simple independent interaction faults optimum

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Optimum Super-simple Mixed Covering arrays of Type a^1b^k-1

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Acta Mathematica Sinica,English Series 2017年第1期33卷 153-164页

作者： Ce SHI School of Mathematics and Information Science Shanghai Lixin University of Commerce Shanghai 201620 Po R. China

A mixed covering array （MCA） of type （v1,v2,..., vk）, denoted by MCAλ（N; t, k, （v1,v2,...,Vk））, is an N × k array with entries in the i-th column from a set Vi of vi symbols and has the property that each N×t sub-array covers all the t-tuples at least A times, where 1≤i ≤ k. An MCAλ（N; t, k, （vl,v2,... ,vk）） is said to be super-simple, if each of its N x （t ＋ 1） sub-arrays con- tains each （t＋1）-tuple at most once. Recently, it was proved by Tang, Yin and the author that an optimum super-simple MCA of type （a, b, b,..., b） is equivalent to a mixed detecting array （DTA） of type （a, b, b,..., b） with optimum size. Such DTAs can be used to generate test suites to identify and determine the interaction faults between the factors in a component-based system. In this paper, some combinatorial constructions of optimum super-simple MCAs of type （a, b, b,..., b） are provided. By employing these constructions, some optimum super-simple MCAs are then obtained. In particu- lar, the spectrum across which optimum super-simple MCA2（2b2; 2, 4, （a, b, b, b））＇s exist, is completely determined, where 2 ≤ a ≤ b.

关键词： Mixed covering arrays super-simple optimum detecting arrays existence

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