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New Computational Paradigms: Changing Conceptions of What is Computable Hardcover – December 12, 2007

ISBN-13: 978-0387360331 ISBN-10: 0387360336 Edition: 2008th

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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)

From the Back Cover

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.


More About the Author

Barry Cooper is Professor of Mathematical Logic at the University of Leeds. A graduate of the University of Oxford, his research follows that of Alan Turing in its focus on the nature of mental and physical computation. Author and editor of numerous books, including Computability Theory, New Computational Paradigms, and Computability in Context, he is a leading advocate of multidisciplinary research at the interface between what is known to be computable, and theoretical and practical incomputability. Chair of the Turing Centenary Committee, which coordinated the international Turing Centenary celebrations, he is President of the Association Computability in Europe, which is responsible for the largest computability-themed international conference series, and chairs the Editorial Board of its Springer book series "Theory and Applications of Computability."

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