Model-Based Testing of Probabilistic Systems

This paper presents a model-based testing framework for probabilistic systems. We provide algorithms to generate, execute and evaluate test cases from a probabilistic requirements model. In doing so, we connect ioco-theory for model-based testing and statistical hypothesis testing: our ioco-style algorithms handle the functional aspects, while statistical methods, using $$\chi ^2$$i¾?2 tests and fitting functions, assess if the frequencies observed during test execution correspond to the probabilities specified in the requirements. Key results of our paper are the classical soundness and completeness properties, establishing the mathematical correctness of our framework; Soundness states that each test case is assigned the right verdict. Completeness states that the framework is powerful enough to discover each probabilistic deviation from the specification, with arbitrary precision. We illustrate the use of our framework via two case studies.