Computability and Complexity TheorySpringer Science & Business Media, 10.12.2011 - 300 Seiten 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. |
Inhalt
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 |
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289 | |
291 | |
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accepting computation accepts algorithm alternating assignment assume begin belongs Boolean bounded called cells claim complexity computable function configuration consider constant construct contains Corollary decidable define Definition denote determine deterministic effective elements encoding enumerable equivalent example execution exists family of circuits finite formula function f given gives graph halts head hierarchy holds Homework important induction initial input word instance integer known language least Lemma length moves nodes Note NP-complete Observe obtain operator oracle output path polynomial polynomial-time positive possible presentable probability problem procedure proof properties Proposition protocol prove query question random Recall reducibility rejects relation requires result runs satisfying scanned simulation space space-bounded steps string Suppose symbol takes tape Theorem time-bounded true Turing machine variables verifier vertex write