Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Bounded Queries in Recursion Theory

  • Book
  • © 1999

Overview

Authors:
  1. William I. Gasarch

    1. Department of Computer Science, University of Maryland, College Park, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Georgia A. Martin

    1. Wheaton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Getting Your Feet Wet

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Basic Concepts

      • William I. Gasarch, Georgia A. Martin
      Pages 3-42

    3. Bounded Queries and the Halting Set

      • William I. Gasarch, Georgia A. Martin
      Pages 43-52

    4. Definitions and Questions

      • William I. Gasarch, Georgia A. Martin
      Pages 53-73

  3. The Complexity of Functions

    1. Front Matter

      Pages 75-75
      Download chapter PDF

    2. The Complexity of C A n

      • William I. Gasarch, Georgia A. Martin
      Pages 77-141

    3. # A n and Other Functions

      • William I. Gasarch, Georgia A. Martin
      Pages 143-182

  4. The Complexity of Sets

    1. Front Matter

      Pages 183-183
      Download chapter PDF

    2. The Complexity of ODD A n and MODm A n

      • William I. Gasarch, Georgia A. Martin
      Pages 185-216

    3. Q Versus QC

      • William I. Gasarch, Georgia A. Martin
      Pages 217-253

    4. Separating and Collapsing Classes

      • William I. Gasarch, Georgia A. Martin
      Pages 255-269

  5. Miscellaneous

    1. Front Matter

      Pages 271-271
      Download chapter PDF

    2. Nondeterministic Complexity

      • William I. Gasarch, Georgia A. Martin
      Pages 273-293

    3. The Literature on Bounded Queries

      • William I. Gasarch, Georgia A. Martin
      Pages 295-324

  6. Back Matter

    Pages 325-353
    Download chapter PDF
Back to top

Keywords

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

Authors and Affiliations

  • Department of Computer Science, University of Maryland, College Park, USA

    William I. Gasarch

  • Wheaton, USA

    Georgia A. Martin

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation