On Monotonicity Testing And The 2 To 2 Games Conjecture
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On Monotonicity Testing And The 2 To 2 Games Conjecture
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Author : Dor Minzer
language : en
Publisher: Morgan & Claypool
Release Date : 2022-12-06
On Monotonicity Testing And The 2 To 2 Games Conjecture written by Dor Minzer and has been published by Morgan & Claypool this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Computers categories.
This book discusses two questions in Complexity Theory: the Monotonicity Testing problem and the 2-to-2 Games Conjecture. Monotonicity testing is a problem from the field of property testing, first considered by Goldreich et al. in 2000. The input of the algorithm is a function, and the goal is to design a tester that makes as few queries to the function as possible, accepts monotone functions and rejects far-from monotone functions with a probability close to 1. The first result of this book is an essentially optimal algorithm for this problem. The analysis of the algorithm heavily relies on a novel, directed, and robust analogue of a Boolean isoperimetric inequality of Talagrand from 1993. The probabilistically checkable proofs (PCP) theorem is one of the cornerstones of modern theoretical computer science. One area in which PCPs are essential is the area of hardness of approximation. Therein, the goal is to prove that some optimization problems are hard to solve, even approximately. Many hardness of approximation results were proved using the PCP theorem; however, for some problems optimal results were not obtained. This book touches on some of these problems, and in particular the 2-to-2 games problem and the vertex cover problem. The second result of this book is a proof of the 2-to-2 games conjecture (with imperfect completeness), which implies new hardness of approximation results for problems such as vertex cover and independent set. It also serves as strong evidence towards the unique games conjecture, a notorious related open problem in theoretical computer science. At the core of the proof is a characterization of small sets of vertices in Grassmann graphs whose edge expansion is bounded away from 1.
Prophets Of Computing
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Author : Dick van Lente
language : en
Publisher: Morgan & Claypool
Release Date : 2022-12-14
Prophets Of Computing written by Dick van Lente and has been published by Morgan & Claypool this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-14 with Computers categories.
When electronic digital computers first appeared after World War II, they appeared as a revolutionary force. Business management, the world of work, administrative life, the nation state, and soon enough everyday life were expected to change dramatically with these machines’ use. Ever since, diverse prophecies of computing have continually emerged, through to the present day. As computing spread beyond the US and UK, such prophecies emerged from strikingly different economic, political, and cultural conditions. This volume explores how these expectations differed, assesses unexpected commonalities, and suggests ways to understand the divergences and convergences. This book examines thirteen countries, based on source material in ten different languages—the effort of an international team of scholars. In addition to analyses of debates, political changes, and popular speculations, we also show a wide range of pictorial representations of "the future with computers."
Logic Automata And Computational Complexity
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Author : Bruce M. Kapron
language : en
Publisher: Morgan & Claypool
Release Date : 2023-05-22
Logic Automata And Computational Complexity written by Bruce M. Kapron and has been published by Morgan & Claypool this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-22 with Computers categories.
Professor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for “his advancement of our understanding of the complexity of computation in a significant and profound way.” This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook’s synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook’s ideas and their enduring impact on the research community. The book also contains biographical material, Cook’s Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.
Current Index To Statistics Applications Methods And Theory
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Author :
language : en
Publisher:
Release Date : 1998
Current Index To Statistics Applications Methods And Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematical statistics categories.
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Analysis Of Boolean Functions
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Author : Ryan O'Donnell
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-05
Analysis Of Boolean Functions written by Ryan O'Donnell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Computers categories.
This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.
Paradigms Of Combinatorial Optimization
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Author : Vangelis Th. Paschos
language : en
Publisher: John Wiley & Sons
Release Date : 2014-08-08
Paradigms Of Combinatorial Optimization written by Vangelis Th. Paschos and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-08 with Mathematics categories.
Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts: - On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity; - Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; - Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.
Beyond The Worst Case Analysis Of Algorithms
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Author : Tim Roughgarden
language : en
Publisher: Cambridge University Press
Release Date : 2021-01-14
Beyond The Worst Case Analysis Of Algorithms written by Tim Roughgarden and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-14 with Computers categories.
Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks.
Computational Complexity
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Author : Subhash Khot
language : en
Publisher:
Release Date : 2014-06-22
Computational Complexity written by Subhash Khot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-22 with categories.
These notes are from a course in Computational Complexity, as offered in Spring 2014 at the Courant Institute of Mathematical Sciences, a school of New York University.The professor for the course was Subhash Khot. Two guest lectures were given by Pratik Worah.The first part of the course includes bread-and-butter complexity. Definitions are given for P and NP, then space complexity, the Polynomial Hierarchy, #P, Interactive Proofs; relations between them will be discussed. The rest of the course consists of some selected topics, including Proof Complexity, Circuit Lower Bounds, Quantum Computation, Communication Complexity, and Probabilistically Checkable Proofs.
Art Gallery Theorems And Algorithms
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Author : Joseph O'Rourke
language : en
Publisher: Oxford University Press, USA
Release Date : 1987
Art Gallery Theorems And Algorithms written by Joseph O'Rourke and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Computers categories.
Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.