Computational Complexity: A Quantitative Perspective, Volume 196 (North-Holland Mathematics Studies)




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Plot : There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various realworld and innocentlooking 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 resourcebounded topological and measuretheoretical 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: averagecomplexity, quantum computation, hardness amplification, resourcebounded measure, the relation between oneway functions and pseudorandom generators, the relation between hard predicates and pseudorandom generators, extractors, derandomization of boundederror probabilistic algorithms, probabilistically checkable proofs, nonapproximability 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 selfcontained and accessible to a wide audience. Large range of important topics including: derandomization techniques, nonapproximability of optimization problems, averagecase complexity, quantum computation, oneway functions and pseudorandom generators, resourcebounded measure and topology.



Author(s) Book :Marius Zimand
E-Book Categories :Computers & Internet; Science & Research; Information Theory; Theory of Computing
Publish Year :2004 Publisher : Elsevier Science
You can check by ISBN10: 0444828419; ISBN13: 9780444828415
Pages :352

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