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Bounded Queries in Recursion Theory

  • William I. Gasarch
  • Georgia A. Martin

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

  • William I. Gasarch
    • 1
  • Georgia A. Martin
    • 2
  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  2. 2.WheatonUSA

Bibliographic information

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