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 eac...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.展开更多
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types ...In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types of super- simple designs which can be applied to codes and designs. In this article, the existence of a super-simple （5, 4）-GDD of group type gU is investigated and it is shown that such a design exists if and only if u ≥ 5, g（u - 2） ≥ 12, and u（u - 1）g^2≡ 0 （mod 5） with some possible exceptions.展开更多
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 DTA...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.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11271280 and 11301342)
文摘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.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371121, 11371308, 11201114, 11301457）.
文摘In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types of super- simple designs which can be applied to codes and designs. In this article, the existence of a super-simple （5, 4）-GDD of group type gU is investigated and it is shown that such a design exists if and only if u ≥ 5, g（u - 2） ≥ 12, and u（u - 1）g^2≡ 0 （mod 5） with some possible exceptions.
基金Supported by National Natural Science Foundation of China(Grant Nos.11301342,11471144)Shanghai Special Research Fund for Training College's Young Teachers(Grant No.ZZlx13001)
文摘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.
