A Theory of Pending Schemas in Combinatorial Testing

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