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Context: Detecting arrays are mathematical structures aimed at faultidentification in combinatorial interaction testing. However, they cannot bedirectly applied to systems that have constraints among test parameters. Suchconstraints are prevalent in real-world systems.  Objectives: This paper proposes Constrained Detecting Arrays (CDAs), anextension of detecting arrays, which can be used for systems with constraints.  Methods: The paper examines the properties and capabilities of CDAs withrigorous arguments. The paper also proposes two algorithms for constructingCDAs: One is aimed at generating minimum CDAs and the other is a heuristicalgorithm aimed at fast generation of CDAs. The algorithms are evaluatedthrough experiments using a benchmark dataset.  Results: Experimental results show that the first algorithm can generateminimum CDAs if a sufficiently long generation time is allowed, and the secondalgorithm can generate minimum or near-minimum CDAs in a reasonable time.  Conclusion: CDAs enhance detecting arrays to be applied to systems withconstraints. The two proposed algorithms have different advantages with respectto the array size and generation time

Constrained Detecting Arrays: Mathematical Structures for Fault Identification in Combinatorial Interaction Testing