Computability Theory An Introduction to Recursion Theory 1st Edition by Herbert Enderton ISBN 9780123849595 0123849594
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ISBN 10: 0123849594
ISBN 13: 9780123849595
Author: Herbert Enderton
Computability Theory: An Introduction to Recursion Theory, provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way.
Frequent historical information presented throughout More extensive motivation for each of the topics than other texts currently available Connects with topics not included in other textbooks, such as complexity theory
Computability Theory An Introduction to Recursion Theory 1st Edition Table of contents:
Chapter 1. The Computability Concept
1.1 The Informal Concept
Exercises
1.2 Formalizations – An Overview
Exercises
Chapter 2. General Recursive Functions
2.1 Primitive Recursive Functions
2.2 Search Operation
Exercises
Chapter 3. Programs and Machines
3.1 Register Machines
3.2 A Universal Program
Exercises
3.3 Register Machines Over Words
Exercises
3.4 Binary Arithmetic
Chapter 4. Recursive Enumerability
4.1 Recursively Enumerable Relations
Exercises
4.2 Parameters
Exercises
Chapter 5. Connections to Logic
5.1 Arithmetical Hierarchy
Exercises
5.2 Definability in Arithmetic
5.3 The Complexity of Truth
Exercises
Chapter 6. Degrees of Unsolvability
6.1 Relative Computability
6.2 Equivalence Relations
6.3 Preordering Relations
6.4 Ordering Degrees
Exercises
6.5 Structure of the Degrees
Exercises
Chapter 7. Polynomial-Time Computability
7.1 Feasible Computability
7.2 P versus NP
7.3 Some Other Complexity Classes
Exercises
Appendix 1. Mathspeak
Appendix 2. Countability
Appendix 3. Decadic Notation
References
Index
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Herbert Enderton,Computability Theory,Recursion Theory