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Recent Advances In Real Complexity And Computation
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Book Synopsis Recent Advances in Real Complexity and Computation by : Luis M. Pardo
Download or read book Recent Advances in Real Complexity and Computation written by Luis M. Pardo and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.
Book Synopsis Complexity and Real Computation by : Lenore Blum
Download or read book Complexity and Real Computation written by Lenore Blum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
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.
Book Synopsis Advances in Computational Complexity Theory by : Jin-yi Cai
Download or read book Advances in Computational Complexity Theory written by Jin-yi Cai and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Recent papers on computational complexity theory * Contributions by some of the leading experts in the field This book will prove to be of lasting value in this fast-moving field as it provides expositions not found elsewhere. The book touches on some of the major topics in complexity theory and thus sheds light on this burgeoning area of research.
Book Synopsis Complexity Theory of Real Functions by : K. Ko
Download or read book Complexity Theory of Real Functions written by K. Ko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. On the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems. In addition, the theoretical studies of the notion of polynomial-time tractability some times also yield interesting new practical algorithms. A typical exam ple is the application of the ellipsoid algorithm to combinatorial op timization problems (see, for example, Lovasz [1986]). On the other hand, it has a strong influence on many different branches of mathe matics, including combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a construc tive proof which admits a polynomial-time algorithm for the solution. One of the examples is the recent work on algorithmic theory of per mutation groups. In the area of numerical computation, there are also two tradi tionally independent approaches: recursive analysis and numerical analysis.
Book Synopsis Theory of Computational Complexity by : Ding-Zhu Du
Download or read book Theory of Computational Complexity written by Ding-Zhu Du and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete treatment of fundamentals and recent advances in complexity theory Complexity theory studies the inherent difficulties of solving algorithmic problems by digital computers. This comprehensive work discusses the major topics in complexity theory, including fundamental topics as well as recent breakthroughs not previously available in book form. Theory of Computational Complexity offers a thorough presentation of the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization, and the application to cryptography. It also examines the theory of nonuniform computational complexity, including the computational models of decision trees and Boolean circuits, and the notion of polynomial-time isomorphism. The theory of probabilistic complexity, which studies complexity issues related to randomized computation as well as interactive proof systems and probabilistically checkable proofs, is also covered. Extraordinary in both its breadth and depth, this volume: * Provides complete proofs of recent breakthroughs in complexity theory * Presents results in well-defined form with complete proofs and numerous exercises * Includes scores of graphs and figures to clarify difficult material An invaluable resource for researchers as well as an important guide for graduate and advanced undergraduate students, Theory of Computational Complexity is destined to become the standard reference in the field.
Book Synopsis Recent Advances in Real Complexity and Computation by : José Luis Montaña
Download or read book Recent Advances in Real Complexity and Computation written by José Luis Montaña and published by . This book was released on 2013 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Computational Complexity by : Ding-Zhu Du
Download or read book Theory of Computational Complexity written by Ding-Zhu Du and published by John Wiley & Sons. This book was released on 2014-06-30 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "... complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity." —Zentralblatt MATH A thorough revision based on advances in the field of computational complexity and readers’ feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered. Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent developments on areas such as NP-completeness theory, as well as: A new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science Additional exercises at varying levels of difficulty to further test comprehension of the presented material End-of-chapter literature reviews that summarize each topic and offer additional sources for further study Theory of Computational Complexity, Second Edition, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.
Book Synopsis Advances in Algorithms, Languages, and Complexity by : Ding-Zhu Du
Download or read book Advances in Algorithms, Languages, and Complexity written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of survey papers in the areas of algorithms, lan guages and complexity, the three areas in which Professor Ronald V. Book has made significant contributions. As a fonner student and a co-author who have been influenced by him directly, we would like to dedicate this book to Professor Ronald V. Book to honor and celebrate his sixtieth birthday. Professor Book initiated his brilliant academic career in 1958, graduating from Grinnell College with a Bachelor of Arts degree. He obtained a Master of Arts in Teaching degree in 1960 and a Master of Arts degree in 1964 both from Wesleyan University, and a Doctor of Philosophy degree from Harvard University in 1969, under the guidance of Professor Sheila A. Greibach. Professor Book's research in discrete mathematics and theoretical com puter science is reflected in more than 150 scientific publications. These works have made a strong impact on the development of several areas of theoretical computer science. A more detailed summary of his scientific research appears in this volume separately.
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: 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
Book Synopsis New Computational Paradigms by : S.B. Cooper
Download or read book New Computational Paradigms written by S.B. Cooper and published by Springer Science & Business Media. This book was released on 2007-11-28 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.
Book Synopsis Theory of Evolutionary Computation by : Benjamin Doerr
Download or read book Theory of Evolutionary Computation written by Benjamin Doerr and published by Springer Nature. This book was released on 2019-11-20 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book reports on recent developments in the theory of evolutionary computation, or more generally the domain of randomized search heuristics. It starts with two chapters on mathematical methods that are often used in the analysis of randomized search heuristics, followed by three chapters on how to measure the complexity of a search heuristic: black-box complexity, a counterpart of classical complexity theory in black-box optimization; parameterized complexity, aimed at a more fine-grained view of the difficulty of problems; and the fixed-budget perspective, which answers the question of how good a solution will be after investing a certain computational budget. The book then describes theoretical results on three important questions in evolutionary computation: how to profit from changing the parameters during the run of an algorithm; how evolutionary algorithms cope with dynamically changing or stochastic environments; and how population diversity influences performance. Finally, the book looks at three algorithm classes that have only recently become the focus of theoretical work: estimation-of-distribution algorithms; artificial immune systems; and genetic programming. Throughout the book the contributing authors try to develop an understanding for how these methods work, and why they are so successful in many applications. The book will be useful for students and researchers in theoretical computer science and evolutionary computing.
Book Synopsis Computational Complexity: A Quantitative Perspective by : Marius Zimand
Download or read book Computational Complexity: A Quantitative Perspective written by Marius Zimand and published by Elsevier Science. This book was released on 2004-07-21 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 probabilistic algorithms, 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.
Book Synopsis Thinking in Complexity by : Klaus Mainzer
Download or read book Thinking in Complexity written by Klaus Mainzer and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity and nonlinearity are prominent features in the evolution of matter, life, and human society. Even our mind seems to be governed by the nonlinear dynamics of the complex networks in our brain. This book considers complex systems in the physical and biological sciences, cognitive and computer sciences, social and economic sciences, and philosophy and history of science. An in terdisciplinary methodology is introduced to explain the emergence of order in nature and mind and in the econ omy and society by common principles. These methods are sometimes said to foreshadow the new sciences of complexity characterizing the scientific deve10pment of the 21 st century. The book critically an alyzes the successes and limits of this approach, its sys tematic foundations, and its historical and philosophical background. An epilogue discusses new standards of eth ical behavior which are demanded by the complex prob lems of nature and mind, economy and society.
Book Synopsis Perspectives in Computational Complexity by : Manindra Agrawal
Download or read book Perspectives in Computational Complexity written by Manindra Agrawal and published by Springer. This book was released on 2014-07-16 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together contributions by leading researchers in computational complexity theory written in honor of Somenath Biswas on the occasion of his sixtieth birthday. They discuss current trends and exciting developments in this flourishing area of research and offer fresh perspectives on various aspects of complexity theory. The topics covered include arithmetic circuit complexity, lower bounds and polynomial identity testing, the isomorphism conjecture, space-bounded computation, graph isomorphism, resolution and proof complexity, entropy and randomness. Several chapters have a tutorial flavor. The aim is to make recent research in these topics accessible to graduate students and senior undergraduates in computer science and mathematics. It can also be useful as a resource for teaching advanced level courses in computational complexity.
Book Synopsis Classical and New Paradigms of Computation and their Complexity Hierarchies by : Benedikt Löwe
Download or read book Classical and New Paradigms of Computation and their Complexity Hierarchies written by Benedikt Löwe and published by Springer Science & Business Media. This book was released on 2007-11-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.
Book Synopsis Recent Advances In Numerical Methods And Applications Ii - Proceedings Of The Fourth International Conference by : Panayot S Vassilevski
Download or read book Recent Advances In Numerical Methods And Applications Ii - Proceedings Of The Fourth International Conference written by Panayot S Vassilevski and published by World Scientific. This book was released on 1999-07-05 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 4th International Conference on Numerical Methods and Applications. The major topics covered include: general finite difference, finite volume, finite element and boundary element methods, general numerical linear algebra and parallel computations, numerical methods for nonlinear problems and multiscale methods, multigrid and domain decomposition methods, CFD computations, mathematical modeling in structural mechanics, and environmental and engineering applications. The volume reflects the current research trends in the specified areas of numerical methods and their applications.
