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Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains

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63 pages
Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains Olivier Bournez Daniel S. Graça Amaury Pouly ENS Lyon May 24, 2011 Olivier Bournez, Daniel S. Graça, Amaury Pouly (ENS Lyon)Solving Analytic Differential Equations in Polynomial Time over Unbounded DomainsMay 24, 2011 ?∞ / 17

  • polynomial time over

  • unbounded domainsmay

  • solving analytic

  • bss model

  • analog computer

  • equations over

  • solving differential

  • blum shub


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Amaury Pouly
Daniel S. Graça
Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains
May 24, 2011
Olivier Bournez
ENS Lyon
lyPoinnalyingAiffeticDaiElertnoisnuqtaMay24,20111/7
Solving differential equations Preliminary remarks Solving differential equations overC Back toR
Outline
1
2
Computing with reals Introduction GPAC Computable analysis Church Thesis
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Many models: Recursive functions Turing machines λ-calculus circuits . . .
The case of integers
71/111
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Many models: Recursive functions Turing machines λ-calculus circuits . . .
The case of integers
71/1
Church Thesis All reasonable discrete models of computation are equivalent.
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Several models: BSS model (Blum Shub Smale) Computable analysis GPAC (General Purpose Analog Computer) . . .
The case of analog computations
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Several models: BSS model (Blum Shub Smale) Computable analysis GPAC (General Purpose Analog Computer) . . . Questions: Church Thesis for analog computers ?
The case of analog computations
172yaM/21102,4
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