Compositionality, Decompositionality and Refinement in Input/Output Conformance Testing
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 component based 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.
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