The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation
Identifieur interne :
000650 ( PascalFrancis/Curation );
précédent :
000649;
suivant :
000651
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
English descriptors
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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A08 | 01 | 1 | ENG | @1 The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation |
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A09 | 01 | 1 | ENG | @1 Theory and applications of models of computation : Third international conference, TAMC 2006, Beijing, China, May 15-20, 2006 : proceedings |
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A11 | 01 | 1 | | @1 BOURNEZ (Olivier) |
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A11 | 02 | 1 | | @1 CAMPAGNOLO (Manuel L.) |
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A11 | 03 | 1 | | @1 GRAQA (Daniel S.) |
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A11 | 04 | 1 | | @1 HAINRY (Emmanuel) |
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A12 | 01 | 1 | | @1 CAI (Jin-yi) @9 ed. |
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A12 | 02 | 1 | | @1 COOPER (S. Barry) @9 ed. |
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A12 | 03 | 1 | | @1 LI (Angsheng) @9 ed. |
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A14 | 03 | | | @1 DM/ISA, Universidade Técnica de Lisboa @2 1349-017 Lisboa @3 PRT @Z 2 aut. |
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A14 | 04 | | | @1 CLC, DM/IST, Universidade Técnica de Lisboa @2 1049-001 Lisboa @3 PRT @Z 2 aut. @Z 3 aut. |
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A14 | 05 | | | @1 DM/FCT, Universidade do Algarve, C. Gambelas @2 8005-139 Faro @3 PRT @Z 3 aut. |
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A14 | 06 | | | @1 Institut National Polytechnique de Lorraine @3 FRA @Z 4 aut. |
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A20 | | | | @1 631-643 |
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A21 | | | | @1 2006 |
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A23 | 01 | | | @0 ENG |
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A43 | 01 | | | @1 INIST @2 16343 @5 354000153627760600 |
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A44 | | | | @0 0000 @1 © 2007 INIST-CNRS. All rights reserved. |
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A45 | | | | @0 24 ref. |
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A47 | 01 | 1 | | @0 07-0531616 |
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A60 | | | | @1 P @2 C |
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A61 | | | | @0 A |
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A64 | 01 | 1 | | @0 Lecture notes in computer science |
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A66 | 01 | | | @0 DEU |
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C01 | 01 | | ENG | @0 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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C02 | 01 | X | | @0 001D02A05 |
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C03 | 01 | X | FRE | @0 Calculabilité @5 06 |
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C03 | 01 | X | ENG | @0 Computability @5 06 |
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C03 | 01 | X | SPA | @0 Calculabilidad @5 06 |
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C03 | 02 | X | FRE | @0 Calculateur analogique @5 18 |
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C03 | 02 | X | ENG | @0 Analog computer @5 18 |
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C03 | 02 | X | SPA | @0 Computadora analógica @5 18 |
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C03 | 03 | X | FRE | @0 Modèle analogique @5 23 |
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C03 | 03 | X | ENG | @0 Analog model @5 23 |
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C03 | 03 | X | SPA | @0 Modelo analógico @5 23 |
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C03 | 04 | X | FRE | @0 Fonction réelle @5 24 |
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C03 | 04 | X | ENG | @0 Real function @5 24 |
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C03 | 04 | X | SPA | @0 Función real @5 24 |
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C03 | 05 | X | FRE | @0 Equation polynomiale @5 25 |
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C03 | 05 | X | ENG | @0 Polynomial equation @5 25 |
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C03 | 05 | X | SPA | @0 Ecuación polinomial @5 25 |
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C03 | 06 | X | FRE | @0 Equation différentielle @5 26 |
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C03 | 06 | X | ENG | @0 Differential equation @5 26 |
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C03 | 06 | X | SPA | @0 Ecuación diferencial @5 26 |
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C03 | 07 | X | FRE | @0 Modélisation @5 27 |
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C03 | 07 | X | ENG | @0 Modeling @5 27 |
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C03 | 07 | X | SPA | @0 Modelización @5 27 |
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N21 | | | | @1 344 |
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N44 | 01 | | | @1 OTO |
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N82 | | | | @1 OTO |
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|
pR |
A30 | 01 | 1 | ENG | @1 TAMC 2006 @2 3 @3 Beijing CHN @4 2006 |
---|
|
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