Download or read book On Probabilistic Proof Systems and Hardness of Approximation written by Jonas Holmerin and published by . This book was released on 2002 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probabilistic Proof Systems written by Oded Goldreich and published by Now Publishers Inc. This book was released on 2008 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various types of probabilistic proof systems have played a central role in the development of computer science in the last couple of decades. These proof systems deviate from the traditional concept of a proof by introducing randomization and interaction into the verification process. Probabilistic proof systems carry an error probability (which is explicitly bounded and can be decreased by repetitions), but they offer various advantages over deterministic proof systems. This primer concentrates on three types of probabilistic proof systems: interactive proofs, zero-knowledge proofs, and probabilistically checkable proofs (PCP). Surveying the basic results regarding these proof systems, the primer stresses the essential role of randomness in each of them.
Download or read book Probabilistic Checking of Proofs and Hardness of Approximation Problems written by Sanjeev Arora and published by . This book was released on 1994 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Weizmann Workshop on Probabilistic Proof Systems written by Mekhon Ṿaitsman le-madaʻ. Dept. of Applied Mathematics and Computer Science and published by . This book was released on 1994 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: " The Weizmann Workshop on Probabilistic Proofs and Applications to Program Checking, Cryptography, and Hardness of Approximation was held at the Weizmann Institute of Science, on January 10- 13, 1994. The following report provides the abstracts of the talks given at the workshop, the list of participants, and relevant references."
Download or read book Modern Cryptography Probabilistic Proofs and Pseudorandomness written by Oded Goldreich and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.
Download or read book Lectures on Proof Verification and Approximation Algorithms written by Ernst W. Mayr and published by Springer. This book was released on 2006-06-08 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms. The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers. These lectures are particularly useful for advanced courses or reading groups on the topic.
Download or read book Efficient Checking of Polynomials and Proofs and the Hardness of Approximation Problems written by Madhu Sudan and published by Boom Koninklijke Uitgevers. This book was released on 1995-12-13 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the author's PhD thesis which was selected as the winning thesis of the 1993 ACM Doctoral Dissertation Competition. The author improved the presentation and included the progress achieved since the thesis was approved by the University of California at Berkeley. This work is a fascinating piece of theoretical computer science research building on deep results from different areas. It provides new theoretical insights and advances applicable techniques in such different areas as computational complexity, efficient (randomized) checking of proofs, programs and polynomials, approximation algorithms, NP-complete optimization, and error-detection and error-correction algorithms in coding theory.
Download or read book Probabilistic Proof Systems written by Oded Goldreich and published by . This book was released on 1996 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Various types of probabilistic proof systems have played a central role in the development of computer science in the last decade. In these notes, we concentrate on three such proof systems -- interactive proofs, zero-knowledge proofs, and probabilistic checkable proofs."
Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Sanjeev Arora and published by Springer. This book was released on 2003-12-15 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, error-correcting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications.
Download or read book Approximation Algorithms for NP hard Problems written by Dorit S. Hochbaum and published by Course Technology. This book was released on 1997 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. APPROXIMATION ALGORITHMS FOR NP-HARD PROBLEMS is intended for computer scientists and operations researchers interested in specific algorithm implementations, as well as design tools for algorithms. Among the techniques discussed: the use of linear programming, primal-dual techniques in worst-case analysis, semidefinite programming, computational geometry techniques, randomized algorithms, average-case analysis, probabilistically checkable proofs and inapproximability, and the Markov Chain Monte Carlo method. The text includes a variety of pedagogical features: definitions, exercises, open problems, glossary of problems, index, and notes on how best to use the book.
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.
Download or read book Ten Lectures on the Probabilistic Method written by Joel Spencer and published by SIAM. This book was released on 1994-01-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties.
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Chandra Chekuri and published by Springer Science & Business Media. This book was released on 2005-08-08 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and the 9th International Workshop on Randomization and Computation, RANDOM 2005, held in Berkeley, CA, USA in August 2005. The volume contains 41 carefully reviewed papers, selected by the two program committees from a total of 101 submissions. Among the issues addressed are design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of approximation and randomness.
Download or read book Proof Verification and the Hardness of Approximation Problems written by International Business Machines Corporation. Research Division and published by . This book was released on 1993 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "The class PCP(r(n), q(n)) consists of all languages L for which there exists a polynomial-time probabilistic oracle machine that uses O(r(n)) random bits, queries O(q(n)) bits of its oracle and behaves as follows: If x [member of] L then there exists an oracle y such that the machine accepts for all random choices but if x [not member of] L then for every oracle y the machine rejects with high probability. Arora and Safra very recently characterized NP as PCP(log n, (log log n)[superscript O(1)]). We improve on their result by showing that NP = PCP(log n, 1). Our result has the following consequences: 1. MAXSNP-hard problems (e.g., metric TSP, MAX-SAT, MAX-CUT) do not have polynomial time approximation schemes unles P=NP. 2. For some [epsilon]> 0 the size of the maximal clique in a graph cannot be approximated within a factor of n[superscript [epsilon]] unless P=NP."
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Ashish Goel and published by Springer. This book was released on 2008-08-28 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the 11th International Wo- shop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2008) and the 12th International Workshop on Randomization and Computation (RANDOM 2008), which took place concurrently at the MIT (M- sachusetts Institute of Technology) in Boston, USA, during August 25–27, 2008. APPROX focuses on algorithmic and complexity issues surrounding the development of e?cient approximate solutions to computationally di?cult problems, and was the 11th in the series after Aalborg (1998), Berkeley (1999), Saarbru ̈cken (2000), Berkeley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 12th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley (1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). Topics of interest for APPROX and RANDOM are: design and analysis of - proximation algorithms, hardness of approximation, small space, sub-linear time, streaming, algorithms, embeddings and metric space methods, mathematical programming methods, combinatorial problems in graphs and networks, game t- ory, markets, economic applications, geometric problems, packing, covering, scheduling, approximate learning, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and - beddings, error-correcting codes, average-case analysis, property testing, com- tational learning theory, and other applications of approximation and randomness.
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Irit Dinur and published by Springer. This book was released on 2009-08-21 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 13th workshop in the series following Bologna (1997), Barcelona (1998),Berkeley(1999),Geneva(2000),Berkeley(2001),Harvard(2002),Prin- ton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), and Boston (2008).
