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The Foundations of Computability Theory

Authors: Robič, Borut

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  • Original, informative view of the development of the fundamental concepts of computability theory
  • Avoids excessive formalism, offering instead intuitive understanding
  • Characterized by appreciation of historical context and motivation of the logical development of the theory presented
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eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-662-44808-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-662-44807-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-662-51601-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy.

This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

About the authors

Prof. Borut Robič received his Ph.D. in Computer Science from the University of Ljubljana in 1993. He is a member of the Faculty of Computer and Information Science of the University of Ljubljana where he leads the Laboratory for Algorithms and Data Structures. He has had guest professorships, fellowships and collaborations with the University of Cambridge, the University of Augsburg, the University of Grenoble, and the Jožef Stefan Institute in Ljubljana. His research interests and teaching experience address algorithms; computability and computational complexity theory; parallel, distributed and grid computing; operating systems; and processor architectures. Prof. Robič coauthored the book "Processor Architecture: From Dataflow to Superscalar and Beyond" (Springer 1999).

Reviews

“The book incorporates many historical, philosophical, and practical concerns closely related to the definitions and core results of the subject. In addition, the book covers enough ground to be able to discuss the finite injury priority method. … The tone is friendly and accessible, and a reader can learn some of the fundamental aspects of computability theory and its history without getting bogged down in technical details.” (Joseph R. Mileti, Mathematical Reviews, September, 2016)

“For the prepared, this is a wonderful blending of history and philosophy, foundations and computation, math and the mystery of the incomplete, undecidable, unknowable, incomputable. … a willing reader will be happy.” (Benjamin Wells, ACM Computing Reviews, April, 2016)

“The main purpose of this book is to provide the reader with a clear and deep understanding of the foundations of computability theory. This goal is fully achieved, because the book is well-written and its reading is very pleasant. … It is a good textbook for undergraduate or beginning graduate students in computer science or mathematics, and I suggest to use it.” (Patrizio Cintioli, zbMATH 1339.03001, 2016)


Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-662-44808-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-662-44807-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-662-51601-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Foundations of Computability Theory
Authors
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-44808-3
DOI
10.1007/978-3-662-44808-3
Hardcover ISBN
978-3-662-44807-6
Softcover ISBN
978-3-662-51601-0
Edition Number
1
Number of Pages
XX, 331
Number of Illustrations
109 b/w illustrations
Topics