Abstract
In a complex component-based system, choices (levels) for components (factors) may interact to cause faults in the system behaviour. When faults may be caused by interactions among few factors at specific levels, covering arrays provide a combinatorial test suite for discovering the presence of faults. While well studied, covering arrays do not enable one to determine the specific levels of factors causing the faults; locating arrays ensure that the results from test suite execution suffice to determine the precise levels and factors causing faults, when the number of such causes is small. Constructions for locating arrays are at present limited to heuristic computational methods and quite specific direct constructions. In this paper three recursive constructions are developed for locating arrays to locate one pairwise interaction causing a fault.
Highlights
IntroductionIt is easy to see that Glaisher’s map is transposition of this sequence of matrices, restricted to partitions into odd or distinct parts, where either the first row or the first column are the only nonzero entries
A nonincreasing sequence of positive integers (λ = (λ1, λ2, . . . , λi) such that λj = n is a partition of n, denoted λ n
We prove results that suggest surprising usefulness for such a simple tool, including the existence of a related statistic that realizes every possible Ramanujan-type congruence for the partition function
Summary
It is easy to see that Glaisher’s map is transposition of this sequence of matrices, restricted to partitions into odd or distinct parts, where either the first row or the first column are the only nonzero entries. Once these matrices are built, a wide array of transformations suggest themselves. Throughout, we mention questions of possible research interest which arise in connection with these ideas
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