Retaining the probabilities in probabilistic testing theory

This paper considers the probabilistic may/must testing theory for processes having external, internal, and probabilistic choices. We observe that the underlying testing equivalence is too strong and distinguishes between processes that are observationally equivalent. The problem arises from the observation that the classical compose-and-schedule approach yields unrealistic overestimation of the probabilities, a phenomenon that has been recently well studied from the point of view of compositionality (de Alfaro/Henzinger/Jhala 2001, Cheung/Lynch/Segala/Vaandrager 2006), in the context of randomized protocols (Chatzikokolakis/Palamidessi 2007), and in probabilistic model checking (Giro/D'Argenio/Ferrer Fioriti 2009). To that end, we propose a new testing theory, aiming at preserving the probability information in a parallel context. The resulting testing equivalence is insensitive to the exact moment the internal and the probabilistic choices occur. We also give an alternative characterization of the testing preorder as a probabilistic ready-trace preorder.