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Computability in context : computation and logic in the real world /

Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, base...

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Bibliographic Details
Corporate Authors: World Scientific (Firm)
Group Author: Cooper, S. B. (S. Barry) (Editor); Sorbi, Andrea, 1956- (Editor)
Published: Imperial College Press ; Distributed by World Scientific Pub. Co.,
Publisher Address: London : Singapore :
Publication Dates: 2011.
Literature type: eBook
Language: English
Subjects:
Computable functions.
Computational intelligence.
Set theory.
Mathematics > Philosophy.
Electronic books.
Online Access: http://www.worldscientific.com/worldscibooks/10.1142/P577#t=toc
Summary: Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier. This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world and how this affects our way of thinking about everyday computational issues.
Carrier Form: 1 online resource (viii,410pages) : illustrations (some color)
Bibliography: Includes bibliographical references.
ISBN: 9781848162778 (electronic bk.)
CLC: O141
Contents: 1. Computation, information, and the arrow of time / P. Adriaans & P. van Emde Boas -- 2. The isomorphism conjecture for NP / M. Agrawal -- 3. 3. The Ershov hierarchy / M. M. Arslanov -- 4. Complexity and approximation in reoptimization / G. Ausiello, V. Bonifaci, & B. Escoffier -- 5. Definability in the real universe / S. B. Cooper -- 6. HF-computability / Y. L. Ershov, V. G. Puzarenko, & A. I. Stukachev -- 7. The mathematics of computing between logic and physics / G. Longo & T. Paul -- 8. Liquid state machines : Motivation, theory, and applications / W. Maass -- 9. Experiments on an internal approach to typed algorithms in analysis / D. Normann -- 10. Recursive functions : An archeological look / P. Odifreddi -- 11. Reverse mathematics and well-ordering principles / M. Rathjen & A. Weiermann -- 12. Discrete transfinite computation models / P. D. Welch.

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