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Progress in Computer Science and Applied Logic

Bounded Queries in Recursion Theory

Authors: Levine, William S., Martin, Georgia

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About this book

One of the major concerns of theoretical computer science is the classifi­ cation of problems in terms of how hard they are. The natural measure of difficulty of a function is the amount of time needed to compute it (as a function of the length of the input). Other resources, such as space, have also been considered. In recursion theory, by contrast, a function is considered to be easy to compute if there exists some algorithm that computes it. We wish to classify functions that are hard, i.e., not computable, in a quantitative way. We cannot use time or space, since the functions are not even computable. We cannot use Turing degree, since this notion is not quantitative. Hence we need a new notion of complexity-much like time or spac~that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function.

Reviews

"Ideal for an advanced undergraduate or beginning graduate student who has some exposure to basic computability theory and wants to see what one can do with it. The questions asked are interesting and can be easily understood and the proofs can be followed without a large amount of training in computability theory."

--Sigact News


Table of contents (10 chapters)

  • Basic Concepts

    Gasarch, William I. (et al.)

    Pages 3-42

  • Bounded Queries and the Halting Set

    Gasarch, William I. (et al.)

    Pages 43-52

  • Definitions and Questions

    Gasarch, William I. (et al.)

    Pages 53-73

  • The Complexity of C n A

    Gasarch, William I. (et al.)

    Pages 77-141

  • # n A and Other Functions

    Gasarch, William I. (et al.)

    Pages 143-182

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4612-0635-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA in USD
  • ISBN 978-0-8176-3966-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA in USD
  • ISBN 978-1-4612-6848-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bounded Queries in Recursion Theory
Authors
Series Title
Progress in Computer Science and Applied Logic
Series Volume
16
Copyright
1999
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0635-4
DOI
10.1007/978-1-4612-0635-4
Hardcover ISBN
978-0-8176-3966-2
Softcover ISBN
978-1-4612-6848-2
Series ISSN
2297-0576
Edition Number
1
Number of Pages
XIII, 353
Topics