Computability and Complexity Theory / Edition 2

Computability and Complexity Theory / Edition 2

5.0 1
by Steven Homer, Alan L. Selman
     
 

"The theory of computing provides computer science with concepts, models, and formalisms for reasoning about the resources needed to carry out computations and about the efficiency of the computations that use these resources. In addition, it provides tools to measure the difficulty of combinatorial problems both absolutely and in comparison with other problems."… See more details below

Overview

"The theory of computing provides computer science with concepts, models, and formalisms for reasoning about the resources needed to carry out computations and about the efficiency of the computations that use these resources. In addition, it provides tools to measure the difficulty of combinatorial problems both absolutely and in comparison with other problems." "Requiring no explicit prerequisite knowledge, Computability and Complexity Theory introduces materials that are the core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations and subsequent chapters moving from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability NP-completeness and relative computability round of the work, which focuses on the limitations of computability and the distinctions between feasible and intractable."--BOOK JACKET.

Read More

Product Details

ISBN-13:
9781461406815
Publisher:
Springer US
Publication date:
12/09/2011
Series:
Texts in Computer Science Series
Edition description:
2nd ed. 2011
Pages:
300
Sales rank:
1,189,727
Product dimensions:
6.14(w) x 9.21(h) x 0.75(d)

Meet the Author

Table of Contents

Preface
1Preliminaries1
1.1Words and Languages1
1.2K-adic Representation2
1.3Partial Functions3
1.4Graphs4
1.5Propositional Logic6
1.6Cardinality8
1.7Elementary Algebra11
2Introduction to Computability22
2.1Turing Machines23
2.2Turing-Machine Concepts26
2.3Variations of Turing Machines28
2.4Church's Thesis34
2.5RAMs36
3Undecidability41
3.1Decision Problems41
3.2Undecidable Problems43
3.3Pairing Functions46
3.4Computably Enumerable Sets47
3.5Halting Problem, Reductions, and Complete Sets50
3.6S-m-n Theorem53
3.7Recursion Theorem55
3.8Rice's Theorem57
3.9Turing Reductions and Oracle Turing Machines59
3.10Recursion Theorem, Continued66
4Introduction to Complexity Theory72
4.1Complexity Classes and Complexity Measures74
4.2Prerequisites77
5Basic Results of Complexity Theory78
5.1Linear Compression and Speedup80
5.2Constructible Functions86
5.3Tape Reduction90
5.4Inclusion Relationships97
5.5Separation Results107
5.6Translation Techniques and Padding111
5.7Relations between the Standard Classes - Continued115
6Nondeterminism and NP-Completeness122
6.1Characterizing NP123
6.2The Class P124
6.3Enumerations126
6.4NP-Completeness128
6.5The Cook-Levin Theorem130
6.6More NP-Complete Problems136
7Relative Computability145
7.1NP-Hardness147
7.2Search Problems151
7.3The Structure of NP153
7.4The Polynomial Hierarchy162
7.5Complete Problems for Other Complexity Classes170
References181
Author Index187
Subject Index191

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >