Covering arrays for some equivalence classes of words

Abstract

Covering arrays for words of length t over a d-letter alphabet are k n × arrays with entries from the alphabet so that for each choice of t columns, each of the d t t-letter words appears at least once among the rows of the selected columns. We study two schemes in which all words are not considered to be different. In the first case known as partitioning hash families, words are equivalent if they induce the same partition of a t element set. In the second case, words of the same weight are equivalent. In both cases, we produce logarithmic upper bounds on the minimum size k k n = ( ) of a covering array. Definitive results for t = 2, 3, 4, as well as general results, are provided. K E Y W O R D S covering arrays, lovász local lemma, partitioning hash families, set partitions, word weight How to cite this article: Cassels J, Godbole A. Covering arrays for some equivalence classes of words. J Combin Des. 2019;27:506-521. https://doi.

Review of Combinatorial Testing Strategy

“…Finally, it is added to a final test suite (FTS) one after the other when all interactions are covered by the FTS (i.e., a horizontal extension). Once completed, new test cases (vertical extension) can be added to obtain maximum coverage of interactions [10,12]. The Parameter Order Strategy (IPO) was developed by Lei and Tai and represents innovative research using the OPAT approach [13,14].…”

“…Variable Strength (VS) extends the uniform Strength. The difference between the uniform Strength and Variable Strength is that it alone guarantees and has more than one interaction strength for generating test cases [10]. Input-Output Relationships (IORs) involve the use of input-output relationship information for interaction tests.…”

“…Several strategies, as well as improved t-way combinatorial testing techniques, have also been developed to optimize any algorithm and to generate smaller test sequences or an almost optimal number of tests. difficult problem [1,9,10]. Many researchers in this area have been encouraged by this scenario.…”