Error dependencies on classes of implementations under testing

The paper discusses the problem of dependency between errors defined by specification and the related problem of test optimization. There is a dependency between errors if a strict subset of errors exists such that any nonconforming implementation (i.e. an implementation containing an error) contains an error from this subset. Accordingly, it is sufficient for the tests to detect errors only from this subset. The most general formal model of test interaction and the reduction type of conformance are suggested, for which dependency between errors is almost absent. Most of the known conformances in various interaction semantics are demonstrated to be special cases of this general model. In this general model, the dependency between errors may occur when any strict subset of the class of all implementations is chosen as a class of implementations under testing. Particular interaction semantics and/or various hypotheses on implementations (specifically, the safety hypothesis), in fact, assume that the implementation under testing should belong to some subclass of (safe) implementations.