Formally comparing user and implementer model-based testing methods

There are several methods to assess the capability of a test suite to detect faults in a potentially wrong system. We explore two methods based on considering some probabilistic information. In the first one, we assume that we are provided with a probabilistic user model. This is a model denoting the probability that the entity interacting with the system takes each available choice. In the second one, we suppose that we have a probabilistic implementer model, that is, a model denoting the probability that the implementer makes each possible fault while constructing the system. We show that both testing scenarios are strongly related. In particular, we prove that any user can be translated into an implementer model in such a way that the optimality of tests is preserved, that is, a test suite is optimal for the user if and only if it is optimal for the resulting implementer. Another translation, working in the opposite direction, fulfills the reciprocal property. Thus, we conclude that any test selection criterium designed for one of these testing problems can be used for the other one, once the model has been properly translated.