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

Olivier Bournez; Manuel L. Campagnolo; Daniel S. Graça; Emmanuel Hainry

doi:10.1007/11750321_60

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

Olivier Bournez
, Manuel L. Campagnolo
, Daniel S. Graça
, Emmanuel Hainry

LORIA and INRIA Lorraine
LORIA Laboratoire Lorrain de Recherche en Informatique et ses Applications
Instituto Superior de Agronomia, Universidade Tecnica de Lisboa
Instituto Superior Técnico
Universidade do Algarve
Nancy Université

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Theory and Applications of Models of Computation - Third International Conference, TAMC 2006, Proceedings
Publisher	Springer Verlag
Pages	631-643
Number of pages	13
ISBN (Print)	3540340211, 9783540340218
DOIs	https://doi.org/10.1007/11750321_60
Publication status	Published - 1 Jan 2006
Externally published	Yes
Event	3rd International Conference on Theory and Applications of Models of Computation, TAMC 2006 - Beijing, China Duration: 15 May 2006 → 20 May 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3959 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Conference on Theory and Applications of Models of Computation, TAMC 2006
Country/Territory	China
City	Beijing
Period	15/05/06 → 20/05/06

Access to Document

10.1007/11750321_60

Cite this

Bournez, O., Campagnolo, M. L., Graça, D. S., & Hainry, E. (2006). The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation. In Theory and Applications of Models of Computation - Third International Conference, TAMC 2006, Proceedings (pp. 631-643). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3959 LNCS). Springer Verlag. https://doi.org/10.1007/11750321_60

Bournez, Olivier ; Campagnolo, Manuel L. ; Graça, Daniel S. et al. / The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation. Theory and Applications of Models of Computation - Third International Conference, TAMC 2006, Proceedings. Springer Verlag, 2006. pp. 631-643 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation",

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.",

author = "Olivier Bournez and Campagnolo, \{Manuel L.\} and Gra{\c c}a, \{Daniel S.\} and Emmanuel Hainry",

year = "2006",

month = jan,

day = "1",

doi = "10.1007/11750321\_60",

language = "English",

isbn = "3540340211",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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booktitle = "Theory and Applications of Models of Computation - Third International Conference, TAMC 2006, Proceedings",

note = "3rd International Conference on Theory and Applications of Models of Computation, TAMC 2006 ; Conference date: 15-05-2006 Through 20-05-2006",

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Bournez, O, Campagnolo, ML, Graça, DS & Hainry, E 2006, The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation. in Theory and Applications of Models of Computation - Third International Conference, TAMC 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3959 LNCS, Springer Verlag, pp. 631-643, 3rd International Conference on Theory and Applications of Models of Computation, TAMC 2006, Beijing, China, 15/05/06. https://doi.org/10.1007/11750321_60

The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation. / Bournez, Olivier; Campagnolo, Manuel L.; Graça, Daniel S. et al.
Theory and Applications of Models of Computation - Third International Conference, TAMC 2006, Proceedings. Springer Verlag, 2006. p. 631-643 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3959 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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M3 - Conference contribution

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Bournez O, Campagnolo ML, Graça DS, Hainry E. The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation. In Theory and Applications of Models of Computation - Third International Conference, TAMC 2006, Proceedings. Springer Verlag. 2006. p. 631-643. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11750321_60

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

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