Optimum super-simple mixed covering arrays of type a ¹ b ^k−1

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• 作者：Ce Shi
• 关键词：Mixed covering arrays ; super ; simple ; optimum ; detecting arrays ; existence
• 刊名：Acta Mathematica Sinica, English Series
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：153-164
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1439-7617
• 卷排序：33

文摘

A mixed covering array (MCA) of type (_v1, v₂,..., v_k), denoted by MCA_λ (N; t, k, (v₁, v₂,..., v_k)), is an N × k array with entries in the i-th column from a set _Vi of v_i symbols and has the property that each N × t sub-array covers all the t-tuples at least λ times, where 1 ≤ i ≤ k. An MCA_λ(N; t, k, (_v1, v₂,..., v_k)) is said to be super-simple, if each of its N × (t + 1) sub-arrays contains 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 particular, the spectrum across which optimum super-simple MCA₂(2b2; 2, 4, (a, b, b, b))′s exist, is completely determined, where 2 ≤ a ≤ b.