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Hypercomputation

Computing Beyond the Church-Turing Barrier

By Apostolos Syropoulos

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This book provides a thorough description of hypercomputation, covering all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine.

Full Description

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  • ISBN13: 978-0-3873-0886-9
  • 270 Pages
  • User Level: Science
  • Publication Date: December 10, 2008
  • Available eBook Formats: PDF
Full Description
Hypercomputation is a relatively new theory of computation that is about computing methods and devices that transcend the so-called Church-Turing thesis. This book will provide a thorough description of the field of hypercomputation covering all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine. Readers of this book will get a deeper understanding of what computability is and why the Church-Turing thesis poses an arbitrary limit to what can be actually computed. Hypercomputing is in and of itself quite a novel idea and as such the book will be interesting in its own right. The most important features of the book, however, will be the thorough description of the various attempts of hypercomputation: from trial-and-error machines to the exploration of the human mind, if we treat it as a computing device.
Table of Contents

Table of Contents

  1. Preface.
  2. Introduction.
  3. On the Church
  4. Turing Thesis.
  5. Early Hypercomputers.
  6. Infinite Time Turing Machines.
  7. Interactive Computing.
  8. Hyperminds.
  9. Computing Real Numbers.
  10. Relativistic and Quantum Hypercomputation.
  11. Natural Computation and Hypercomputation.
  12. Appendix A. Interactability and Hypercomputation.
  13. Appendix B.
  14. Socio
  15. Economical Implications.
  16. Appendix C. A Précis of Topology and Differential Geometry.
  17. Bibliography.
  18. People Index.
  19. Subject Index.
Errata

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