New Computational Paradigms
Changing Conceptions of What is Computable
Editors: Cooper, S. Barry, Löwe, Benedikt, Sorbi, Andrea (Eds.)
Free Preview- Explores new developments in the theory and practice of computation from a mathematical and predominantly logical perspective
- Covers topics ranging from classical computability to complexity, biocomputing and quantum computing
- Written not only for specialists, but also with a broader audience in mind
- Contributors are all prominent scholars and worldwide known specialists
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- About this book
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In recent years, classical computability has expanded beyond its original scope to address issues related to computability and complexity in algebra, analysis, and physics. The deep interconnection between "computation" and "proof" has originated much of the most significant work in constructive mathematics and mathematical logic of the last 70 years. Moreover, the increasingly compelling necessity to deal with computability in the real world (such as computing on continuous data, biological computing, and physical models) has brought focus to new paradigms of computation that are based on biological and physical models. These models address questions of efficiency in a radically new way and even threaten to move the so-called Turing barrier, i.e. the line between the decidable and the un-decidable.
This book examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. The book opens with an introduction by Andrew Hodges, the Turing biographer, who analyzes the pioneering work that anticipated recent developments concerning computation’s allegedly new paradigms. The remaining material covers traditional topics in computability theory such as relative computability, theory of numberings, and domain theory, in addition to topics on the relationships between proof theory, computability, and complexity theory. New paradigms of computation arising from biology and quantum physics are also discussed, as well as the computability of the real numbers and its related issues.
This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.
- Reviews
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From the reviews:
“It is addressed to researcher and graduate students … . All contributions to the book have been rigorously refereed, and the standards with respect to layout, references … are high. … This is a piece of excellent pedagogical work. The paper is hereby recommended. … I personally find very readable and informative. … I enjoyed reading these papers, and I assume they are all right when we take them for what they are … .” (Lars Kristiansen, Studia Logica, Vol. 97, 2011)
- Table of contents (20 chapters)
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Alan Turing, Logical and Physical
Pages 3-15
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Computability and Numberings
Pages 19-34
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Computation as Conversation
Pages 35-58
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Computation Paradigms in Light of Hilbert's Tenth Problem
Pages 59-85
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Elementary Algorithms and Their Implementations
Pages 87-118
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Table of contents (20 chapters)
- Download Preface 1 PDF (74.1 KB)
- Download Sample pages 1 PDF (284.5 KB)
- Download Table of contents PDF (86 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- New Computational Paradigms
- Book Subtitle
- Changing Conceptions of What is Computable
- Editors
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- S. Barry Cooper
- Benedikt Löwe
- Andrea Sorbi
- Copyright
- 2008
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer-Verlag New York
- eBook ISBN
- 978-0-387-68546-5
- DOI
- 10.1007/978-0-387-68546-5
- Hardcover ISBN
- 978-0-387-36033-1
- Softcover ISBN
- 978-1-4419-2263-2
- Edition Number
- 1
- Number of Pages
- XIV, 560
- Topics
