Continuous-Time Probabilistic KLAIM

The design of languages supporting network programming is a necessary step towards the formalisation of distributed and mobile computing. The existence of an abstract semantic framework constitutes the basis for a formal analysis of such systems. The KLAIM paradigm [5] provides such a semantic framework by introducing basic concepts and primitives addressing the key aspects of the coordination of interacting located processes. We extend this basic paradigm with probabilistic constructs with the aim of introducing a semantic basis for a quantitative analysis of networks. A quantitative analysis allows in general for the consideration of more “realistic” situations. For example, a probabilistic analysis allows for establishing the security of a system up to a given tolerance factor expressing how much the system is actually vulnerable. This is in contrast to a qualitative analysis which typically might be used to validate the absolute security of a given system. In a distributed environment quantitative analysis is also of a great practical use in the consideration of timing issues which involve the asynchronous communications among processes running with different clocks. In a security setting these issues are relevant e.g. for the analysis and prevention of denial of service attacks, which involve the delaying of time-critical operations [9]. In our probabilistic version of KLAIM, which we call pKLAIM, we introduce probabilities in a number of ways. At the local level, we introduce probabilistic parallel and choice operators. In addition we use probabilistic