Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: A Survey of Binary Covering Arrays. | A Survey of Binary Covering Arrays Jim Lawrence George Mason University Fairfax VA 22030 lawrence@ Raghu N. Kacker National Institute of Standards and Technology Gaithersburg MD 20899 Yu Lei University of Texas at Arlington Arlington TX 76019 ylei@ D. Richard Kuhn National Institute of Standards and Technology Gaithersburg MD 20899 Michael Forbes Massachusetts Institute of Technology Cambridge MA 02139 miforbes@ Submitted Jun 21 2010 Accepted Mar 31 2011 Published Apr 7 2011 Mathematics Subject Classifications 05B20 05B30 Abstract Binary covering arrays of strength t are 0-1 matrices having the property that for each t columns and each of the possible 2 sequences of t 0 s and 1 s there exists a row having that sequence in that set of t columns. Covering arrays are an important tool in certain applications for example in software testing. In these applications the number of columns of the matrix is dictated by the application and it is desirable to have a covering array with a small number of rows. Here we survey some of what is known about the existence of binary covering arrays and metho ds of producing them including both explicit constructions and search techniques. THE ELECTRONIC JOURNAL OF COMBINATORICS 18 2011 P84 1 1. Introduction. An n X k vi . Vk -valued covering array of strength t where n t and k are integers satisfying n 1 and 1 t k and vi . vk is a vector of k integers Vj 2 is a matrix of size n X k such that entries in column j come from a set Vj of parameter values of cardinality Vj and each n X t submatrix having columns indexed by elements of a set A c 1 . k where A t contains all of the different Hje A Vj possible rows that can be formed by choosing the entry with index j G A from the j-th set of parameter values. Suppose A ji . jt c 1 . k where ji j2 . jt. We call the pair A x X xj1 . Xjt being a vector whose entries are indexed by A a t-tuple. If y yi . yk is a vector of length k we
