On the Discriminating Power of Testing Equivalences for Reactive Probabilistic Systems: Results and Open Problems

International audienceTesting equivalences have been deeply investigated on fully nondeterministic processes, as well as on processes featuring probabilities and internal nondeterminism. This is not the case with reactive probabilistic processes, for which it is only known that the discriminating power of probabilistic bisimilarity is achieved when admitting a copying capability within tests. In this paper, we introduce for reactive probabilistic processes three testing equivalences without copying, which are respectively based on reactive probabilistic tests, fully nondeterministic tests, and nondeterministic and probabilistic tests. We show that the three testing equivalences are strictly finer than probabilistic failure-trace equivalence, and that the one based on nondeterministic and probabilistic tests is strictly finer than the other two, which are incomparable with each other. Moreover, we provide a number of facts that lead us to conjecture that (i) may testing and must testing coincide on reactive probabilistic processes and (ii) nondeterministic and probabilistic tests reach the same discriminating power as probabilistic bisimilarity

On the Discriminating Power of Passivation and Higher-Order Interaction

none3noThis paper studies the discriminating power offered by higher-order concurrent languages, and contrasts this power with those offered by higher-order sequential languages (à la lambda-calculus) and by first-order concurrent languages (à la CCS). The concurrent higher-order languages that we focus on are Higher-Order pi-calculus (HOpi), which supports higher-order communication, and an extension of HOpi with passivation, a simple higher-order construct that allows one to obtain location-dependent process behaviours. The comparison is carried out by providing embeddings of first-order processes into the various languages, and then examining the resulting contextual equivalences induced on such processes. As first-order processes we consider both ordinary Labeled Transition Systems (LTSs) and Reactive Probabilistic Labeled Transition Systems (RPLTSs). The hierarchy of discriminating powers so obtained for RPLTSs is finer than that for LTSs. For instance, in the LTS case, the additional discriminating power offered by passivation in concurrency is captured, in sequential languages, by the difference between the call-by-name and call-by-value evaluation strategies of an extended typed lambda-calculus.mixedBernardo, Marco; Sangiorgi, Davide; Vignudelli, ValeriaBernardo, Marco; Sangiorgi, Davide; Vignudelli, Valeri