Overview
- Provides a uniquely concise introduction to these subjects
- Includes numerous examples and exercises
- Progresses from general to deeper models of computability
Part of the book series: Undergraduate Topics in Computer Science (UTICS)
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Table of contents (11 chapters)
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Front Matter
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Background
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Front Matter
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Computability Theory
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Front Matter
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Computational Complexity Theory
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Front Matter
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Back Matter
Keywords
About this book
This is a book about computation, something which is ubiquitous in the modern world. More precisely, it examines computability theory and computational complexity theory. Computability theory is the part of mathematics and computer science which seeks to clarify what we mean by computation or algorithm. When is there a computational solution possible to some question? How can we show that none is possible? How computationally hard is the question we are concerned with? Arguably, this area lead to the development of digital computers. (Computational) complexity theory is an intellectual heir of computability theory. Complexity theory is concerned with understanding what resources are needed for computation, where typically we would measure the resources in terms of time and space. Can we perform some task in a feasible number of steps? Can we perform some algorithm with only a limited memory? Does randomness help? Are there standard approaches to overcoming computational difficulty?
Authors and Affiliations
About the author
Rodney Downey is an Emeritus Professor at Victoria University of Wellington, NZ. He is the co-author of the Springer books, Fundamentals of Parameterized Complexity, and Algorithmic Randomness and Complexity. He has won many prizes for his work, including (twice) the Shoenfield Prize for writing, as well as the Rutherford Medal, New Zealand’s premier science award.
Bibliographic Information
Book Title: Computability and Complexity
Book Subtitle: Foundations and Tools for Pursuing Scientific Applications
Authors: Rod Downey
Series Title: Undergraduate Topics in Computer Science
DOI: https://doi.org/10.1007/978-3-031-53744-8
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Softcover ISBN: 978-3-031-53743-1Published: 11 May 2024
eBook ISBN: 978-3-031-53744-8Published: 10 May 2024
Series ISSN: 1863-7310
Series E-ISSN: 2197-1781
Edition Number: 1
Number of Pages: XXVIII, 346
Number of Illustrations: 17 b/w illustrations
Topics: Theory of Computation, Mathematical Logic and Foundations, Computer Applications, Complex Systems