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Introducti onIn the reactive model [Pnu85) of classical concurrency theory, a process reacts to stimuli presented by its environment. A mechanistic view of the reactive model has been given by Milner [Mil80) in terms of button pushing ezperiments. The environment or observer experiments on a process by attempting to depress one of several buttons that the process possesses as its interface to the outside world. The experiment succeeds if the button is unlocked and therefore goes down; otherwise the experiment fails. In response to a successful experiment, the process makes an internal state transition and is then ready for further experimentation.The reactive model has been adopted by Larsen and Skou [LS89) for probabilistic processes: a buttonpressing experiment succeeds, with probability 1, or else fails. If successful, the process makes an internal state transition according to a probability distribution associated with the depressed button.In the probabilistic case, it is interesting to consider a more "probabilistic" form of experimentation we call the generative model. In this setting, an observer may attempt to depress more than one button at a time.•Research supported by NSF Grant CCR-8704309. CH2897- ed.a c. ukNow the process is more or less on equal footing with its environment, and will decide, according to a prescribed probability distribution, which button if any will go down. In :response to a successful outcome, this same probability distribution, conditioned by the process's choice of button, will govern the internal state transition made by the process. Figure 1. For P, an a-or b-experiment will succeed with probability 1, whereas a c-expe:riment will fail. In the case of an aexperiment, P will branch left with probability t and right with probability i· Note that no information is given about the relative probability of performing an a-action versus a b-action in P's initial state.For the generative process Q, if the observer simultaneously attempts to depress the a and b buttons, Q will unlock its a-button with probability i and its b-button with probability l-In the former case, Q will branch left with probability t and right with probability ~,

Abstract. We propose a process algebra for wireless mesh networks that combines novel treatments of local broadcast, conditional unicast and data structures. In this framework, we model the Ad-hoc On-Demand Distance Vector (AODV) routing protocol and (dis)prove crucial properties such as loop freedom and packet delivery.

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We investigate equivalence notions for concurrent systems. We consider "linear time" approaches where the system behaviour is characterised as the set of possible runs as well as "branching time" approaches where the conflict structure of systems is taken into account. We show that the usual interleaving equivalences, and also the equivalences based on steps (multisets of concurrently executed actions) are not preserved by refinement of atomic actions. We prove that "linear time" partial order semantics, where causality in runs is explicit, is invariant under refinement. Finally, we consider various bisimulation equivalences based on partial orders and show that the strongest one of them is preserved by refinement whereas the others are not.

We develop a general testing scenario for probabilistic processes, giving rise to two theories: probabilistic may testing and probabilistic must testing. These are applied to a simple probabilistic version of the process calculus CSP. We examine the algebraic theory of probabilistic testing, and show that many of the axioms of standard testing are no longer valid in our probabilistic setting; even for non-probabilistic CSP processes, the distinguishing power of probabilistic tests is much greater than that of standard tests. We develop a method for deriving inequations valid in probabilistic may testing based on a probabilistic extension of the notion of simulation. Using this, we obtain a complete axiomatisation for non-probabilistic processes subject to probabilistic may testing.

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