Computational Complexity And Property Testing

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Computational Complexity and Property Testing

Author : Oded Goldreich
Publisher : Springer Nature
ISBN 13 : 3030436624
Total Pages : 391 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Computational Complexity and Property Testing by : Oded Goldreich

Download or read book Computational Complexity and Property Testing written by Oded Goldreich and published by Springer Nature. This book was released on 2020-04-03 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of studies in the areas of complexity theory and property testing. The 21 pieces of scientific work included were conducted at different times, mostly during the last decade. Although most of these works have been cited in the literature, none of them was formally published before. Within complexity theory the topics include constant-depth Boolean circuits, explicit construction of expander graphs, interactive proof systems, monotone formulae for majority, probabilistically checkable proofs (PCPs), pseudorandomness, worst-case to average-case reductions, and zero-knowledge proofs. Within property testing the topics include distribution testing, linearity testing, lower bounds on the query complexity (of property testing), testing graph properties, and tolerant testing. A common theme in this collection is the interplay between randomness and computation.

Introduction to Property Testing

Author : Oded Goldreich
Publisher : Cambridge University Press
ISBN 13 : 1107194059
Total Pages : 473 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Introduction to Property Testing by : Oded Goldreich

Download or read book Introduction to Property Testing written by Oded Goldreich and published by Cambridge University Press. This book was released on 2017-11-23 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive and authoritative introduction to property testing, the study of super-fast algorithms for the structural analysis of large quantities of data in order to determine global properties. This book can be used both as a reference book and a textbook, and includes numerous exercises.

Computational Complexity and Property Testing

Author : Oded Goldreich
Publisher :
ISBN 13 : 9783030436636
Total Pages : 391 pages
Book Rating : 4.4/5 (366 download)

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Book Synopsis Computational Complexity and Property Testing by : Oded Goldreich

Download or read book Computational Complexity and Property Testing written by Oded Goldreich and published by . This book was released on 2020 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of studies in the areas of complexity theory and property testing. The 21 pieces of scientific work included were conducted at different times, mostly during the last decade. Although most of these works have been cited in the literature, none of them was formally published before. Within complexity theory the topics include constant-depth Boolean circuits, explicit construction of expander graphs, interactive proof systems, monotone formulae for majority, probabilistically checkable proofs (PCPs), pseudorandomness, worst-case to average-case reductions, and zero-knowledge proofs. Within property testing the topics include distribution testing, linearity testing, lower bounds on the query complexity (of property testing), testing graph properties, and tolerant testing. A common theme in this collection is the interplay between randomness and computation.

Computational Complexity

Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Computational Complexity by : Sanjeev Arora

Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Computational Complexity

Author : Oded Goldreich
Publisher : Cambridge University Press
ISBN 13 : 9780521884730
Total Pages : 632 pages
Book Rating : 4.8/5 (847 download)

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Book Synopsis Computational Complexity by : Oded Goldreich

Download or read book Computational Complexity written by Oded Goldreich and published by Cambridge University Press. This book was released on 2008-04-28 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive perspective to modern topics in complexity theory, which is a central field of the theoretical foundations of computer science. It addresses the looming question of what can be achieved within a limited amount of time with or without other limited natural computational resources. Can be used as an introduction for advanced undergraduate and graduate students as either a textbook or for self-study, or to experts, since it provides expositions of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness and probabilistic proof systems.

Introduction to Property Testing

Author : Oded Goldreich
Publisher : Cambridge University Press
ISBN 13 : 1108152120
Total Pages : 473 pages
Book Rating : 4.1/5 (81 download)

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Book Synopsis Introduction to Property Testing by : Oded Goldreich

Download or read book Introduction to Property Testing written by Oded Goldreich and published by Cambridge University Press. This book was released on 2017-11-23 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Property testing is concerned with the design of super-fast algorithms for the structural analysis of large quantities of data. The aim is to unveil global features of the data, such as determining whether the data has a particular property or estimating global parameters. Remarkably, it is possible for decisions to be made by accessing only a small portion of the data. Property testing focuses on properties and parameters that go beyond simple statistics. This book provides an extensive and authoritative introduction to property testing. It provides a wide range of algorithmic techniques for the design and analysis of tests for algebraic properties, properties of Boolean functions, graph properties, and properties of distributions.

Communication Complexity (for Algorithm Designers)

Author : Tim Roughgarden
Publisher : Foundations and Trends (R) in Theoretical Computer Science
ISBN 13 : 9781680831146
Total Pages : 206 pages
Book Rating : 4.8/5 (311 download)

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Book Synopsis Communication Complexity (for Algorithm Designers) by : Tim Roughgarden

Download or read book Communication Complexity (for Algorithm Designers) written by Tim Roughgarden and published by Foundations and Trends (R) in Theoretical Computer Science. This book was released on 2016-05-11 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals mostly with impossibility results - lower bounds on what can be accomplished by algorithms. However, the perspective is unapologetically that of an algorithm designer. The reader will learn lower bound technology on a "need-to-know" basis, guided by fundamental algorithmic problems that we care about.

Property Testing

Author : Arnab Bhattacharyya
Publisher : Springer Nature
ISBN 13 : 981168622X
Total Pages : 434 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Property Testing by : Arnab Bhattacharyya

Download or read book Property Testing written by Arnab Bhattacharyya and published by Springer Nature. This book was released on 2022-03-08 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces important results and techniques in property testing, where the goal is to design algorithms that decide whether their input satisfies a predetermined property in sublinear time, or even in constant time – that is, time is independent of the input size. This book consists of three parts. The first part provides an introduction to the foundations of property testing. The second part studies the testing of specific properties on strings, graphs, functions, and constraint satisfaction problems. Vectors and matrices over real numbers are also covered. The third part is more advanced and explains general conditions, including full characterizations, under which properties are constant-query testable. The first and second parts of the book are intended for first-year graduate students in computer science. They should also be accessible to undergraduate students with the adequate background. The third part can be used by researchers or ambitious graduate students who want to gain a deeper theoretical understanding of property testing.

P, NP, and NP-Completeness

Author : Oded Goldreich
Publisher : Cambridge University Press
ISBN 13 : 1139490095
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis P, NP, and NP-Completeness by : Oded Goldreich

Download or read book P, NP, and NP-Completeness written by Oded Goldreich and published by Cambridge University Press. This book was released on 2010-08-16 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.

Studies in Complexity and Cryptography

Author : Oded Goldreich
Publisher : Springer
ISBN 13 : 3642226701
Total Pages : 573 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Studies in Complexity and Cryptography by : Oded Goldreich

Download or read book Studies in Complexity and Cryptography written by Oded Goldreich and published by Springer. This book was released on 2011-08-03 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of 36 pieces of scientific work in the areas of complexity theory and foundations of cryptography: 20 research contributions, 13 survey articles, and 3 programmatic and reflective viewpoint statements. These so far formally unpublished pieces were written by Oded Goldreich, some in collaboration with other scientists. The articles included in this book essentially reflect the topical scope of the scientific career of Oded Goldreich now spanning three decades. In particular the topics dealt with include average-case complexity, complexity of approximation, derandomization, expander graphs, hashing functions, locally testable codes, machines that take advice, NP-completeness, one-way functions, probabilistically checkable proofs, proofs of knowledge, property testing, pseudorandomness, randomness extractors, sampling, trapdoor permutations, zero-knowledge, and non-iterative zero-knowledge. All in all, this potpourri of studies in complexity and cryptography constitutes a most valuable contribution to the field of theoretical computer science centered around the personal achievements and views of one of its outstanding representatives.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Property Testing

Author : Oded Goldreich
Publisher : Springer Science & Business Media
ISBN 13 : 3642163661
Total Pages : 370 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Property Testing by : Oded Goldreich

Download or read book Property Testing written by Oded Goldreich and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Property Testing is the study of super-fast algorithms for approximate decision making. This volume features work presented at a mini-workshop on property testing that took place January 2010 at the Institute for Computer Science, Tsinghua University, China.

Tutorials on the Foundations of Cryptography

Author : Yehuda Lindell
Publisher : Springer
ISBN 13 : 331957048X
Total Pages : 461 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Tutorials on the Foundations of Cryptography by : Yehuda Lindell

Download or read book Tutorials on the Foundations of Cryptography written by Yehuda Lindell and published by Springer. This book was released on 2017-04-05 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate textbook of advanced tutorials on the theory of cryptography and computational complexity. In particular, the chapters explain aspects of garbled circuits, public-key cryptography, pseudorandom functions, one-way functions, homomorphic encryption, the simulation proof technique, and the complexity of differential privacy. Most chapters progress methodically through motivations, foundations, definitions, major results, issues surrounding feasibility, surveys of recent developments, and suggestions for further study. This book honors Professor Oded Goldreich, a pioneering scientist, educator, and mentor. Oded was instrumental in laying down the foundations of cryptography, and he inspired the contributing authors, Benny Applebaum, Boaz Barak, Andrej Bogdanov, Iftach Haitner, Shai Halevi, Yehuda Lindell, Alon Rosen, and Salil Vadhan, themselves leading researchers on the theory of cryptography and computational complexity. The book is appropriate for graduate tutorials and seminars, and for self-study by experienced researchers, assuming prior knowledge of the theory of cryptography.

Algorithmic and Analysis Techniques in Property Testing

Author : Dana Ron
Publisher : Now Publishers Inc
ISBN 13 : 1601983182
Total Pages : 151 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Algorithmic and Analysis Techniques in Property Testing by : Dana Ron

Download or read book Algorithmic and Analysis Techniques in Property Testing written by Dana Ron and published by Now Publishers Inc. This book was released on 2010 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Property testing algorithms are ultra"-efficient algorithms that decide whether a given object (e.g., a graph) has a certain property (e.g., bipartiteness), or is significantly different from any object that has the property. To this end property testing algorithms are given the ability to perform (local) queries to the input, though the decisions they need to make usually concern properties with a global nature. In the last two decades, property testing algorithms have been designed for many types of objects and properties, amongst them, graph properties, algebraic properties, geometric properties, and more. In this article we survey results in property testing, where our emphasis is on common analysis and algorithmic techniques. Among the techniques surveyed are the following: a) The self-correcting approach, which was mainly applied in the study of property testing of algebraic properties; b) The enforce and test approach, which was applied quite extensively in the analysis of algorithms for testing graph properties (in the dense-graphs model), as well as in other contexts; c) Szemeredi's Regularity Lemma, which plays a very important role in the analysis of algorithms for testing graph properties (in the dense-graphs model); d) The approach of Testing by implicit learning, which implies efficient testability of membership in many functions classes. e) Algorithmic techniques for testing properties of sparse graphs, which include local search and random walks.

Property Testing

Author : Dana Ron
Publisher : Now Publishers Inc
ISBN 13 : 1601981821
Total Pages : 113 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Property Testing by : Dana Ron

Download or read book Property Testing written by Dana Ron and published by Now Publishers Inc. This book was released on 2008 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey focuses on results for testing properties of functions that are of interest to the learning theory community.

Computational Complexity

Author : IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing
Publisher : IEEE
ISBN 13 : 9780769514680
Total Pages : 205 pages
Book Rating : 4.5/5 (146 download)

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Book Synopsis Computational Complexity by : IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing

Download or read book Computational Complexity written by IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing and published by IEEE. This book was released on 2002 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains information on computational mathematics as presented at the 17th IEEE Annual Conference on Computational Complexity (CCC 2002).

Higher-Order Fourier Analysis and Applications

Author : Hamed Hatami
Publisher :
ISBN 13 : 9781680835922
Total Pages : 230 pages
Book Rating : 4.8/5 (359 download)

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Book Synopsis Higher-Order Fourier Analysis and Applications by : Hamed Hatami

Download or read book Higher-Order Fourier Analysis and Applications written by Hamed Hatami and published by . This book was released on 2019-09-26 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher-order Fourier Analysis and Applications provides an introduction to the field of higher-order Fourier analysis with an emphasis on its applications to theoretical computer science. Higher-order Fourier analysis is an extension of the classical Fourier analysis. It has been developed by several mathematicians over the past few decades in order to study problems in an area of mathematics called additive combinatorics, which is primarily concerned with linear patterns such as arithmetic progressions in subsets of integers. The monograph is divided into three parts: Part I discusses linearity testing and its generalization to higher degree polynomials. Part II present the fundamental results of the theory of higher-order Fourier analysis. Part III uses the tools developed in Part II to prove some general results about property testing for algebraic properties. It describes applications of the theory of higher-order Fourier analysis in theoretical computer science, and, to this end, presents the foundations of this theory through such applications; in particular to the area of property testing.