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Zimand M. — Computational Complexity: A Quantitative Perspective
Zimand M. — Computational Complexity: A Quantitative Perspective



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Название: Computational Complexity: A Quantitative Perspective

Автор: Zimand M.

Аннотация:

There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various real-world and innocent-looking tasks are infeasible. In fact, "bad news" is a relative term, and, indeed, in some situations (e.g., in cryptography), we want an adversary to not be able to perform a certain task. However, a "bad news" result does not automatically become useful in such a scenario. For this to happen, its hardness features have to be quantitatively evaluated and shown to manifest extensively.

The book undertakes a quantitative analysis of some of the major results in complexity that regard either classes of problems or individual concrete problems. The size of some important classes are studied using resource-bounded topological and measure-theoretical tools. In the case of individual problems, the book studies relevant quantitative attributes such as approximation properties or the number of hard inputs at each length.

One chapter is dedicated to abstract complexity theory, an older field which, however, deserves attention because it lays out the foundations of complexity. The other chapters, on the other hand, focus on recent and important developments in complexity. The book presents in a fairly detailed manner concepts that have been at the centre of the main research lines in complexity in the last decade or so, such as: average-complexity, quantum computation, hardness amplification, resource-bounded measure, the relation between one-way functions and pseudo-random generators, the relation between hard predicates and pseudo-random generators, extractors, derandomization of bounded-error probabilisticalgorithms, probabilistically checkable proofs, non-approximability of optimization problems, and others.

The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.

· Emphasis is on relevant quantitative attributes of important results in complexity.
· Coverage is self-contained and accessible to a wide audience.
· Large range of important topics including: derandomization techniques, non-approximability of optimization problems, average-case complexity, quantum computation, one-way functions and pseudo-random generators, resource-bounded measure and topology.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 356

Добавлена в каталог: 04.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Thakur, M.      313
Time complexity      3
Topological space      12
TOT      61 66 68
Trakhtenbrot, B.      49
Trevisan, L.      224
Triangle inequality      148 149
Triangle property      164
Turing machine      1
Turing machine, language accepted by      2
Turing machine, nondeterministic      3
Turing machine, oracle      52
Turing machine, probabilistic      8
Umans, C      224
Union theorem      45 49
Unitary matrix      113
Unitary transformation      113 119
Unitary transformation, simple      126
Vadhan, S.      224
Vazirani, U.      140 224
VC      240
Verifier      268 269
Vertex cover      240 244 258 261 267 282 287
von Neumann, J.      224
Wang, J.      108
Watrous, J.      141
Weak source      156
Weight assignment      242
Weight assignment, canonical      243
Weight assignment, positive      242
Weitenfurter, H.      140
Welch, L.      223
Wigderson, A.      223 315
Winklman, K.      49
XOR lemma      224
Yannakakis, M.      313 315
Yao, A.      127 222—224
Young, P.      49 50
Zimand, M.      50 107 141 313 315
Zuckerman, D.      224 315
|x|      13
1 2 3
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