Computability and Complexity Theory / Edition 2

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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.
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Editorial Reviews

From the Publisher
From the reviews:

"The difference between this new introductory graduate textbook in theoretical computer science and other texts is that the authors have chosen to concentrate on computability theory and computational complexity theory. They motivate this focus by pointing out that most students have been introduced to the theory of automata and formal languages as undergraduates. The topics are treated in depth and in full formal detail. Explicit homework assignments are tightly integrated into the exposition of the material." —Computing Reviews

"This book is intended for use in a modern graduate course in the theory of computing. … Mainly all old classical complexity results as well as a relatively recent result that space-bounded classes are closed under complements are included into the book. The textbook is self-contained. A list of useful homework problems is appended to each chapter. The book is well written and is recommended to students as well as specialists in theoretical computer science." (Anatoly V. Anisimov, Zentralblatt MATH, Vol. 1033 (8), 2004)

"This book is a solid textbook suited for one- or two-semester graduate courses on the theory of computing. …The authors are two leading researchers in the field of theoretical computer sciences, most notably complexity theory. … This textbook is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates and professionals involved in theoretical computer science, complexity theory and computability will find this book an essential and practical learning tool." (André Grosse, The Computer Journal, Vol. 45 (4), 2002)

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Product Details

  • ISBN-13: 9781461406815
  • Publisher: Springer US
  • Publication date: 12/9/2011
  • Series: Texts in Computer Science Series
  • Edition description: 2nd ed. 2011
  • Edition number: 2
  • Pages: 300
  • Sales rank: 1,115,946
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.75 (d)

Table of Contents

Preface
1 Preliminaries 1
1.1 Words and Languages 1
1.2 K-adic Representation 2
1.3 Partial Functions 3
1.4 Graphs 4
1.5 Propositional Logic 6
1.6 Cardinality 8
1.7 Elementary Algebra 11
2 Introduction to Computability 22
2.1 Turing Machines 23
2.2 Turing-Machine Concepts 26
2.3 Variations of Turing Machines 28
2.4 Church's Thesis 34
2.5 RAMs 36
3 Undecidability 41
3.1 Decision Problems 41
3.2 Undecidable Problems 43
3.3 Pairing Functions 46
3.4 Computably Enumerable Sets 47
3.5 Halting Problem, Reductions, and Complete Sets 50
3.6 S-m-n Theorem 53
3.7 Recursion Theorem 55
3.8 Rice's Theorem 57
3.9 Turing Reductions and Oracle Turing Machines 59
3.10 Recursion Theorem, Continued 66
4 Introduction to Complexity Theory 72
4.1 Complexity Classes and Complexity Measures 74
4.2 Prerequisites 77
5 Basic Results of Complexity Theory 78
5.1 Linear Compression and Speedup 80
5.2 Constructible Functions 86
5.3 Tape Reduction 90
5.4 Inclusion Relationships 97
5.5 Separation Results 107
5.6 Translation Techniques and Padding 111
5.7 Relations between the Standard Classes - Continued 115
6 Nondeterminism and NP-Completeness 122
6.1 Characterizing NP 123
6.2 The Class P 124
6.3 Enumerations 126
6.4 NP-Completeness 128
6.5 The Cook-Levin Theorem 130
6.6 More NP-Complete Problems 136
7 Relative Computability 145
7.1 NP-Hardness 147
7.2 Search Problems 151
7.3 The Structure of NP 153
7.4 The Polynomial Hierarchy 162
7.5 Complete Problems for Other Complexity Classes 170
References 181
Author Index 187
Subject Index 191
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