Optimal locating arrays for at most two faults

Shi, Ce; Tang, Yu; Yin, Jianxing

doi:10.1007/s11425-011-4307-5

Cited by 22 publications

(11 citation statements)

References 8 publications

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“…Some mathematical properties of locating arrays have been revealed in this work, and the locating arrays have been applied in the studies [39], [40]. Some upper bounds of specific locating arrays have been proved by Shi et al [41] and Tang et al [42]. Studies [43], [44] made some contributions on construction methods of locating arrays.…”

Section: Non-adaptive Classmentioning

confidence: 99%

A Theory of Pending Schemas in Combinatorial Testing

Niu

Nie

et al. 2022

IIEEE Trans. Software Eng.

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Combinatorial Testing (CT) is an effective testing technique for detecting failures which are triggered by the interactions of various factors that influence the behaviour of a system. Although many studies in CT have designed elaborate test suites (called covering arrays) to systemically check each possible factor interaction, they provide weak support to locate the concrete failure-inducing interactions, i.e., the Minimal Failure-causing Schemas (MFS). To this end, a variety of MFS identification approaches have been proposed. However, as this study reveals, these approaches suffer from various issues such as cannot identify multiple overlapping MFSs, cannot handle MFSs with high degrees, cannot be applied to systems with large number of parameters, etc. These issues are essentially caused by the exponential computing complexity of checking every interaction in the test cases. Therefore, they can only focus on a subset of all the possible interactions, resulting in many interactions unnoticed. Ignoring these unnoticed interactions could potentially cause failures that have never been systematically checked. Hence, it is beneficial for MFS identification approaches to identify these interactions. In order to account for these unnoticed interactions in CT, this study introduces the notion of pending schema, based on which a theoretical framework of CT schemas is established. In particular, we formally define the determinability of a schema in CT with respect to given information; as such, the yet-to-be determined schemas are exactly the pending schemas. The relationships between the different schemas (faulty, healthy, and pending) and test cases are also theoretically analyzed. Based on which, we further propose three formulas, along with three corresponding algorithms, for the identification of the pending schemas in failing test cases, and formally prove their correctness. As a result, we reduce the complexity of obtaining pending schemas with respect to the number of factors that may have influences on the software.

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Section: Non-adaptive Classmentioning

confidence: 99%

A Theory of Pending Schemas in Combinatorial Testing

Niu

Nie

et al. 2022

IIEEE Trans. Software Eng.

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“…Martínez et al [30] develop adaptive analogues and establish feasibility conditions for a locating array to exist. In [36] and [37] the minimum number of rows in a locating array is determined when the number of factors is quite small. Recursive constructions when (d, t) = (1, 2) are given in [14].…”

Section: Array Definitionmentioning

confidence: 99%

Disjoint spread systems and fault location

Colbourn,

Fan,

Horsley

2021

Preprint

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When k factors each taking one of v levels may affect the correctness or performance of a complex system, a test is selected by setting each factor to one of its levels and determining whether the system functions as expected (passes the test) or not (fails). In our setting, each test failure can be attributed to at least one faulty (factor, level) pair. A nonadaptive test suite is a selection of such tests to be executed in parallel. One goal is to minimize the number of tests in a test suite from which we can determine which (factor, level) pairs are faulty, if any. In this paper, we determine the number of tests needed to locate faults when exactly one (or at most one) pair is faulty. To do this, we address an equivalent problem, to determine how many set partitions of a set of size N exist in which each partition contains v classes and no two classes in the partitions are equal.

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“…They analyzed the mathematical properties of these arrays. As [3], most of the studies on DAs and LAs focus on their mathematical aspects [16,17,18,19,20,21]. The application to screening experiments for TCP throughput in a mobile wireless network was reported in [22,23].…”

Section: Related Workmentioning

confidence: 99%

Constrained detecting arrays for fault localization in combinatorial testing

Jin

Shi

Tsuchiya

2020

Proceedings of the 35th Annual ACM Symposium on Applied Computing

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Detecting Arrays (DAs) are mathematical objects that enable fault localization in combinatorial interaction testing. Each row of a DA serves as a test case, whereas a whole DA is treated as a test suite. In real-world testing problems, it is often the case that some constraints exist among test parameters. In this paper, we show that it may be impossible to construct a DA using only constraintsatisfying test cases. The reason for this is that a set of some faulty interactions may always mask the effect of other faulty interactions in the presence of constraints. Based on this observation, we propose the notion of Constrained Detecting Arrays (CDAs) to adapt DAs to practical situations. The definition of CDAs requires that all rows of a CDA must satisfy the constraints and the same fault localization capability as the DA must hold except for such inherently undetectable faults. We then propose a computational method for constructing CDAs. Experimental results obtained by using a program that implements the method show that the method was able to produce CDAs within a reasonable time for practical problem instances. CCS CONCEPTS • Software and its engineering → Software testing and debugging; • Mathematics of computing → Combinatorial optimization.

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Optimal locating arrays for at most two faults

Cited by 22 publications

References 8 publications

A Theory of Pending Schemas in Combinatorial Testing

A Theory of Pending Schemas in Combinatorial Testing

Disjoint spread systems and fault location

Constrained detecting arrays for fault localization in combinatorial testing

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