Formalisation of Computability of Operators and Real-Valued Functionals via Domain Theory

Based on an effective theory of continuous domains, notions of computability for operators and real-valued functionals defined on the class of continuous functions are introduced. Definability and semantic characterisation of computable functionals are given. Also we propose a recursion scheme which is a suitable tool for formalisation of complex systems, such as hybrid systems. In this framework the trajectories of continuous parts of hybrid systems can be represented by computable functionals.

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