Computability in Context: Computation and Logic in the Real World

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World Scientific, 2011 - Computers - 410 pages
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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. The list of contributors includes: S Abramsky, P Adriaans, M Agrawal, M Arslanov, G Ausiello, J Diaz, Y Ershov, G Longo, W Maass, I Nemeti, A Nerode, D Normann, G Odifreddi, M Rathjen, G Rozenberg, M Vardi, and P Welch.
 

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Contents

3 The Ershov Hierarchy M M Arslanov
49
4 Complexity and Approximation in Reoptimization G Ausiello V Bonifaci B Escoffer
101
5 Definability in the Real Universe S B Cooper
131
6 HFComputability Y L Ershov V G Puzarenko A I Stukachev
169
7 The Mathematics of Computing between Logic and Physics G Longo T Paul
243
Motivation Theory and Applications W Maass
275
9 Experiments on an Internal Approach to Typed Algorithms in Analysis D Normann
297
An Archeological Look P Odifreddi
329
11 Reverse Mathematics and Wellordering Principles M Rathjen A Weiermann
351
12 Discrete Transfinite Computation Models P D Welch
371
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