# Bounded Queries in Recursion Theory

Book

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

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

### 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

• Book Title Bounded Queries in Recursion Theory
• Authors William Levine
Georgia Martin
• Series Title Progress in Computer Science and Applied Logic
• DOI https://doi.org/10.1007/978-1-4612-0635-4
• Copyright Information Birkhäuser Boston 1999
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Hardcover ISBN 978-0-8176-3966-2
• Softcover ISBN 978-1-4612-6848-2
• eBook ISBN 978-1-4612-0635-4
• Edition Number 1
• Number of Pages XIII, 353
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
Industry Sectors
Engineering

## 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