# Bounded Queries in Recursion Theory

• William I. Gasarch
• Georgia A. Martin
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

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

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0635-4
• Copyright Information Birkhäuser Boston 1999
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-1-4612-6848-2
• Online ISBN 978-1-4612-0635-4
• Buy this book on publisher's site