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Formalisation of Computability of Operators and RealValued Functionals via Domain Theory
 Proceedings of CCA2000
"... Based on an eective theory of continuous domains, notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced. Denability and semantic characterisation of computable functionals are given. Also we propose a recursion scheme which is a ..."
Abstract

Cited by 3 (3 self)
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Based on an eective theory of continuous domains, notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced. Denability 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. 1
Semantic Characterisations of Secondorder Computability Over the Real Numbers
 LNCS
, 2001
"... We propose semantic characterisations of secondorder computability over the reals based on denability theory. Notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced via domain theory. We consider the reals with and without equal ..."
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Cited by 2 (2 self)
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We propose semantic characterisations of secondorder computability over the reals based on denability theory. Notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced via domain theory. We consider the reals with and without equality and prove theorems which connect computable operators and realvalued functionals with validity of nite formulas. 1
Generalised Computability and an Application to Hybrid Systems
 LNCS
, 2001
"... We investigate the concept of generalised computability of operators and functionals dened on the set of continuous functions, rstly introduced in [9]. By working in the reals, with equality and without equality, we study properties of generalised computable operators and functionals. Also we pr ..."
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Cited by 1 (1 self)
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We investigate the concept of generalised computability of operators and functionals dened on the set of continuous functions, rstly introduced in [9]. By working in the reals, with equality and without equality, we study properties of generalised computable operators and functionals. Also we propose an interesting application to formalisation of hybrid systems. We obtain some class of hybrid systems, which trajectories are computable in the sense of computable analysis.