Beyond Zeno-behaviour

When modelling and analysing hybrid systems using techniques from computing science we may encounter problems with so-called Zeno-behaviour. This is the phenomenon that an innite number of events accumulates before a nite time (Zeno-time). When this happens the standard techniques from computing science fail to dis-tinguish between events that happen after that sequence of events. Many of those techniques have a semantics based on labelled transi-tion systems. In this article, we concentrate on those transition systems and try to nd a solution for the Zeno-problem. We rst introduce transi-tions over innite sequences, since an innite number of events needs to be described. Then we (re-)dene a notion of convergence over sequences in a metric space. Considering a transition system with a metric state space and transitions labelled by sequences we can dene a notion of prex- and accumulation-closedness. Finally within prex-and accumulation-closed transition systems, bisimilarity turns out to distinguish between various kinds of transnite behaviour. The bounc-ing ball, an example from hybrid system theory, is used to illustrate the relevance of these new denitions. 1

An Interactive Viewer for Mathematical Content Based On Type Theory

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