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The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

Identifieur interne : 005746 ( Main/Merge ); précédent : 005745; suivant : 005747

The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

Auteurs : Olivier Bournez [France] ; Manuel L. Campagnolo [Portugal] ; Daniel S. Graqa [Portugal] ; Emmanuel Hainry [France]

Source :

Lecture notes in computer science [ 0302-9743 ] ; 2006.

RBID : Pascal:07-0531616

Descripteurs français

Pascal (Inist)
- Calculabilité, Calculateur analogique, Modèle analogique, Fonction réelle, Equation polynomiale, Equation différentielle, Modélisation.

English descriptors

KwdEn :
- Analog computer, Analog model, Computability, Differential equation, Modeling, Polynomial equation, Real function.

Abstract

In this paper we revisit one of the first models of analog computation, Shannon's General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPAC-computability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial differential equations then we show that all real computable functions can be defined by such models.

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Pascal:07-0531616

Le document en format XML

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<front><div type="abstract" xml:lang="en">In this paper we revisit one of the first models of analog computation, Shannon's General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPAC-computability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial differential equations then we show that all real computable functions can be defined by such models.</div>
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The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri