Computability and Complexity Theory

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Springer Science & Business Media, Dec 9, 2011 - Computers - 300 pages
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This volume 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 off the work, which focuses on the limitations of computability and the distinctions between feasible and intractable. Topics and features: *Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes *Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner; for example, about complements of complexity classes, search problems, and intermediate problems in NP *Provides key mathematical background information, including sections on logic and number theory and algebra *Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes With its accessibility and well-devised organization, this text/reference 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 the book an essential and practical learning tool.
 

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Contents

Chapter 1 Preliminaries
1
Chapter 2 Introduction to Computability
23
Chapter 3 Undecidability
41
Chapter 4 Introduction to Complexity Theory
74
Chapter 5 Basic Results of Complexity Theory
81
Chapter 6 Nondeterminism and NPCompleteness
123
Chapter 7 Relative Computability
145
Chapter 8 Nonuniform Complexity
181
Chapter 9 Parallelism
200
Chapter 10 Probabilistic Complexity Classes
225
Chapter 11 Introduction to Counting Classes
247
Chapter 12 Interactive Proof Systems
261
References
283
Author Index
289
Subject Index
291
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