A Statistical Approach to Test Stochastic and Probabilistic Systems

In this paper we introduce a formal framework to test systems where non-deterministic decisions are probabilistically quantified and temporal information is defined by using random variables. We define an appropriate extension of the classical finite state machines formalism, widely used in formal testing approaches, to define the systems that we are interested in. First, we define a conformance relation to establish, with respect to a given specification, what a good implementation is. In order to decide whether a system is conforming, we apply different statistic techniques to determine whether the (unknown) probabilities and random variables governing the behaviour of the implementation match the (known) ones of the specification. Next, we introduce a notion of test case. Finally, we give an alternative characterization of the previous conformance relation based on how a set of test is passed by the implementation.