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© 1999

Bounded Queries in Recursion Theory

Book

Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 16)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Getting Your Feet Wet

    1. Front Matter
      Pages 1-1
    2. William I. Gasarch, Georgia A. Martin
      Pages 3-42
    3. William I. Gasarch, Georgia A. Martin
      Pages 43-52
    4. William I. Gasarch, Georgia A. Martin
      Pages 53-73
  3. The Complexity of Functions

    1. Front Matter
      Pages 75-75
    2. William I. Gasarch, Georgia A. Martin
      Pages 77-141
    3. William I. Gasarch, Georgia A. Martin
      Pages 143-182
  4. The Complexity of Sets

    1. Front Matter
      Pages 183-183
    2. William I. Gasarch, Georgia A. Martin
      Pages 185-216
    3. William I. Gasarch, Georgia A. Martin
      Pages 217-253
    4. William I. Gasarch, Georgia A. Martin
      Pages 255-269
  5. Miscellaneous

    1. Front Matter
      Pages 271-271
    2. William I. Gasarch, Georgia A. Martin
      Pages 273-293
    3. William I. Gasarch, Georgia A. Martin
      Pages 295-324
  6. Back Matter
    Pages 325-353

About this book

Introduction

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.

Keywords

Computability Theory Notation algorithms complexity computer computer science simulation theoretical computer science time

Authors and affiliations

  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  2. 2.WheatonUSA

Bibliographic information

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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