Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains

Olivier Bournez

Description

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

Sujets

• Purpose
• Analog computer

Informations

• Publié par: pefav
• Nombre de lectures: 35
• Langue: English

Extrait

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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

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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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And

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