Customized Testing for Probabilistic Systems

In order to test the correctness of an IUT (implementation under test) with respect to a specification, testing its whole behavior is desirable but unfeasible. In some situations, testing the behavior of the IUT assuming that it is stimulated by a given usage model is more appropriate. Though considering this approach to test functional behaviors consists simply in testing a subset of the IUT, to study the probabilistic behavior of systems by using this customized testing approach leads to some new possibilities. If usage models specify the probabilistic behavior of stimuli and specifications define the probabilistic behavior of reactions to these stimuli, then, by composing them, the probabilistic behavior of any behavior is completely specified. So, after a finite set of behaviors of the IUT is checked, we can compute an upper bound of the probability that a user following the usage model finds an error in the IUT. This can be done by considering the worst case scenario, that is, that any unchecked behavior is wrong.