The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation
Identifieur interne :
000383 ( PascalFrancis/Corpus );
précédent :
000382;
suivant :
000384
The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation
Auteurs : Olivier Bournez ;
Manuel L. Campagnolo ;
Daniel S. Graqa ;
Emmanuel HainrySource :
-
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.
Notice en format standard (ISO 2709)
Pour connaître la documentation sur le format Inist Standard.
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| A01 | 01 | 1 | | @0 0302-9743 |
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| A05 | | | | @2 3959 |
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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 | 01 | | | @1 INRIA Lorraine @3 FRA @Z 1 aut. |
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| A14 | 02 | | | @1 LORIA (UMR 7503 CNRS-INPL-INRIA-Nancy2-UHP), Campus scientifique, BP 239 @2 54506 Vandoeuvre-Lès-Nancy @3 FRA @Z 1 aut. @Z 4 aut. |
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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. |
|---|
| 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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| A44 | | | | @0 0000 @1 © 2007 INIST-CNRS. All rights reserved. |
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| A47 | 01 | 1 | | @0 07-0531616 |
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| A60 | | | | @1 P @2 C |
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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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| 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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Format Inist (serveur)
| NO : | PASCAL 07-0531616 INIST |
|---|
| ET : | The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation |
|---|
| AU : | BOURNEZ (Olivier); CAMPAGNOLO (Manuel L.); GRAQA (Daniel S.); HAINRY (Emmanuel); CAI (Jin-yi); COOPER (S. Barry); LI (Angsheng) |
|---|
| AF : | INRIA Lorraine/France (1 aut.); LORIA (UMR 7503 CNRS-INPL-INRIA-Nancy2-UHP), Campus scientifique, BP 239/54506 Vandoeuvre-Lès-Nancy/France (1 aut., 4 aut.); DM/ISA, Universidade Técnica de Lisboa/1349-017 Lisboa/Portugal (2 aut.); CLC, DM/IST, Universidade Técnica de Lisboa/1049-001 Lisboa/Portugal (2 aut., 3 aut.); DM/FCT, Universidade do Algarve, C. Gambelas/8005-139 Faro/Portugal (3 aut.); Institut National Polytechnique de Lorraine/France (4 aut.) |
|---|
| DT : | Publication en série; Congrès; Niveau analytique |
|---|
| SO : | Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 2006; Vol. 3959; Pp. 631-643; Bibl. 24 ref. |
|---|
| LA : | Anglais |
|---|
| EA : | 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. |
|---|
| CC : | 001D02A05 |
|---|
| FD : | Calculabilité; Calculateur analogique; Modèle analogique; Fonction réelle; Equation polynomiale; Equation différentielle; Modélisation |
|---|
| ED : | Computability; Analog computer; Analog model; Real function; Polynomial equation; Differential equation; Modeling |
|---|
| SD : | Calculabilidad; Computadora analógica; Modelo analógico; Función real; Ecuación polinomial; Ecuación diferencial; Modelización |
|---|
| LO : | INIST-16343.354000153627760600 |
|---|
| ID : | 07-0531616 |
|---|
Links to Exploration step
Pascal:07-0531616
Le document en format XML
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<term>Differential equation</term>
<term>Modeling</term>
<term>Polynomial equation</term>
<term>Real function</term>
</keywords><keywords scheme="Pascal" xml:lang="fr"><term>Calculabilité</term>
<term>Calculateur analogique</term>
<term>Modèle analogique</term>
<term>Fonction réelle</term>
<term>Equation polynomiale</term>
<term>Equation différentielle</term>
<term>Modélisation</term>
</keywords><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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</fA11><fA11 i1="03" i2="1"><s1>GRAQA (Daniel S.)</s1>
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<sZ>4 aut.</sZ>
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<sZ>2 aut.</sZ>
</fA14><fA14 i1="04"><s1>CLC, DM/IST, Universidade Técnica de Lisboa</s1>
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</fA14><fA14 i1="05"><s1>DM/FCT, Universidade do Algarve, C. Gambelas</s1>
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</fA14><fA14 i1="06"><s1>Institut National Polytechnique de Lorraine</s1>
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<ET>The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation</ET>
<AU>BOURNEZ (Olivier); CAMPAGNOLO (Manuel L.); GRAQA (Daniel S.); HAINRY (Emmanuel); CAI (Jin-yi); COOPER (S. Barry); LI (Angsheng)</AU>
<AF>INRIA Lorraine/France (1 aut.); LORIA (UMR 7503 CNRS-INPL-INRIA-Nancy2-UHP), Campus scientifique, BP 239/54506 Vandoeuvre-Lès-Nancy/France (1 aut., 4 aut.); DM/ISA, Universidade Técnica de Lisboa/1349-017 Lisboa/Portugal (2 aut.); CLC, DM/IST, Universidade Técnica de Lisboa/1049-001 Lisboa/Portugal (2 aut., 3 aut.); DM/FCT, Universidade do Algarve, C. Gambelas/8005-139 Faro/Portugal (3 aut.); Institut National Polytechnique de Lorraine/France (4 aut.)</AF>
<DT>Publication en série; Congrès; Niveau analytique</DT>
<SO>Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 2006; Vol. 3959; Pp. 631-643; Bibl. 24 ref.</SO>
<LA>Anglais</LA>
<EA>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.</EA>
<CC>001D02A05</CC>
<FD>Calculabilité; Calculateur analogique; Modèle analogique; Fonction réelle; Equation polynomiale; Equation différentielle; Modélisation</FD>
<ED>Computability; Analog computer; Analog model; Real function; Polynomial equation; Differential equation; Modeling</ED>
<SD>Calculabilidad; Computadora analógica; Modelo analógico; Función real; Ecuación polinomial; Ecuación diferencial; Modelización</SD>
<LO>INIST-16343.354000153627760600</LO>
<ID>07-0531616</ID>
</server>
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