Formalization of test experiments

Formal methods for testing conformance of the system under examination to its specification are examined. The operational interaction semantics is specified by a special testing machine that formally determines the testing capabilities. A set of theoretically powerful and practically important capabilities is distinguished that can be reduced to the observation of external actions and refusals (the absence of external actions). The novelties are as follows. (1) Parameterization of the semantics by the families of observable and not observable refusals, which makes it possible to take into account various constraints on the (correct) interactions. (2) Destruction as a forbidden action, which is possible but should not be performed in the case of a correct interaction. (3) Modeling of the divergence by the Δ-action, which also should be avoided in the case of a correct interaction. On the basis of this semantics, the concept of safe testing, the implementation safety hypothesis, and the safe conformance relation are proposed. The safe conformance relation corresponds to the principle of independent observations: a behavior of an implementation is correct or incorrect independently of its other possible behaviors. For a more narrow class of interactions, another version of the semantics based on the ready traces may be used along with the corresponding conformance relation. Some propositions concerning the relationships between the conformance relations under various semantics are formulated. The completion transformation that solves the problem of the conformance relation reflexivity and a monotone transformation that solves the monotonicity problem (preservation of the conformance under composition) are defined.