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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 ..."
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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 3 (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.
Effective Model Theory via the ΣDefinability Approach?
"... Abstract. We present an approach to abstract computability based on the notion of Σdefinability, and survey some results on effective model theory which are obtained within this framework. 1 ..."
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Cited by 1 (0 self)
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Abstract. We present an approach to abstract computability based on the notion of Σdefinability, and survey some results on effective model theory which are obtained within this framework. 1
Siberian Branch of the Russian Academy of Sciences,
"... Abstract. This paper extends the logical approach to computable analysis via Σ–definability to higher type continuous data such as functionals and operators. We employ definability theory to introduce computability of functionals from arbitrary domain to the real numbers. We show how this concept w ..."
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Abstract. This paper extends the logical approach to computable analysis via Σ–definability to higher type continuous data such as functionals and operators. We employ definability theory to introduce computability of functionals from arbitrary domain to the real numbers. We show how this concept works in particular cases. 1
This document in subdirectoryRS/02/26/ Fixed Points on Abstract Structures without the Equality Test
, 909
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
A Logical Approach to Specification of Hybrid Systems
"... . The main subject of our investigation is behaviour of the continuous components of hybrid systems. By a hybrid system we mean a network of digital and analog devices interacting at discrete times. A firstorder logical formalisation of hybrid systems is proposed in which the trajectories of th ..."
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. The main subject of our investigation is behaviour of the continuous components of hybrid systems. By a hybrid system we mean a network of digital and analog devices interacting at discrete times. A firstorder logical formalisation of hybrid systems is proposed in which the trajectories of the continuous components are presented by majorantcomputable functionals. 1 Introduction In the recent time, attention to the problems of exact mathematical formalisation of complex systems such as hybrid systems is constantly raised. By a hybrid system we mean a network of digital and analog devices interacting at discrete times. An important characteristic of hybrid systems is that they incorporate both continuous components, usually called plants, as well as digital components, i.e. digital computers, sensors and atuators controlled by programs. These programs are designed to select, control, and supervise the behaviours of the continuous components. Modelling, design, and investigation...