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A Note on the Approximation of Weak Probabilistic Bisimulation

The need for flexible and formal approaches to the comparison of different process models is motivated in several application domains and with respect to different system properties. They can be helpful to compare a web service with some desired qualitative/quantitative service description, to relate an implemented software architecture to a reference dependable architectural model, and to reveal the performability impact of one component over the whole system through the comparison of the two system views that are obtained by activating/deactivating the component (this is generally called noninterference analysis). As a further step towards the flexibility of equivalence checking based techniques, we advocate an approach that relies on an approximate notion of weak probabilistic bisimulation, through which to provide a measure of the approximation and diagnostic information supporting exact methods such as numerical analysis and state space minimization. Comparing different process models is a frequently used approach to the analysis of system requirements in practical application domains. In order to bridge the gap between rigid equivalence checking techniques and more relaxed distinguishability oriented requirements of real systems, in the last decade much attention has been paid on approximation methods [5,9,4,7,10,2]. This can be done in a quantitative framework where fine-grain models describe, e.g., probability distributions of events or their timed behaviors. For instance, some of the proposals cited above deal with probabilistic notions of behavioral equivalence for deciding if two process models behave almost (up to small fluctuations) the same or, more formally, for measuring the distance between probabilistic transition systems. Based on this idea, one well-established approach uses pseudometrics, which give a measure of the similarity of systems that are not equivalent (see e.g. [7,9]). An alternative approach has been addressed in [10] in the framework of security analysis and of purely generative probabilistic systems. There, the quantifiable amount of distinguishability between process models is defined via a notion of approximate confinement, corresponding to a statistical measure of the power of the observer.