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9781848162457

Computability in Context : Computation and Logic in the Real World

by ;
  • ISBN13:

    9781848162457

  • ISBN10:

    1848162456

  • Format: Hardcover
  • Copyright: 2009-02-28
  • Publisher: Textstream

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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.

Table of Contents

Prefacep. v
Computation, Information, and the Arrow of Timep. 1
The Isomorphism Conjecture for NPp. 19
The Ershov Hierarchyp. 49
Complexity and Approximation in Reoptimizationp. 101
Definability in the Real Universep. 131
HF-Computabilityp. 169
The Mathematics of Computing between Logic and Physicsp. 243
Liquid State Machines: Motivation, Theory, and Applicationsp. 275
Experiments on an Internal Approach to Typed Algorithms in Analysisp. 297
Recursive Functions: An Archeological Lookp. 329
Reverse Mathematics and Well-ordering Principlesp. 351
Discrete Transfinite Computation Modelsp. 371
Table of Contents provided by Ingram. All Rights Reserved.

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