We propose an input/output conformance testing theory utilizing Modal Interface Automata with Input Refusals (IR-MIA) as novel behavioral formalism for both the specification and the implementation under test. A modal refinement relation on IR-MIA allows distinguishing between obligatory and allowed output behaviors, as well as between implicitly underspecified and explicitly forbidden input behaviors. The theory therefore supports positive and negative conformance testing with optimistic and pessimistic environmental assumptions. We further show that the resulting conformance relation on IR-MIA, called modal-irioco, enjoys many desirable properties concerning componentbased behaviors. First, modal-irioco is preserved under modal refinement and constitutes a preorder under certain restrictions which can be ensured by a canonical input completion for IR-MIA. Second, under the same restrictions, modal-irioco is compositional with respect to parallel composition of IR-MIA with multi-cast and hiding. Finally, the quotient operator on IR-MIA, as the inverse to parallel composition, facilitates decompositionality in conformance testing to solve the unknown-component problem.
We present an adaptation of input/output conformance (ioco) testing principles to families of similar implementation variants as appearing in product line engineering. Our proposed product line testing theory relies on Modal Interface Automata (MIA) as behavioral specification formalism. MIA enrich I/O-labeled transition systems with may/must modalities to distinguish mandatory from optional behavior, thus providing a semantic notion of intrinsic behavioral variability. In particular, MIA constitute a restricted, yet fully expressive subclass of I/O-labeled modal transition systems, guaranteeing desirable refinement and compositionality properties. The resulting modal-ioco relation defined on MIA is preserved under MIA refinement, which serves as variant derivation mechanism in our product line testing theory. As a result, modal-ioco is proven correct in the sense that it coincides with traditional ioco to hold for every derivable implementation variant. Based on this result, a family-based product line conformance testing framework can be established.
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