Limits Of Computation
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Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
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
Hypercomputation
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Author : Apostolos Syropoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Hypercomputation written by Apostolos Syropoulos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Computers categories.
Hypercomputation is a relatively new theory of computation that is about computing methods and devices that transcend the so-called Church-Turing thesis. This book will provide a thorough description of the field of hypercomputation covering all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine. Readers of this book will get a deeper understanding of what computability is and why the Church-Turing thesis poses an arbitrary limit to what can be actually computed. Hypercomputing is in and of itself quite a novel idea and as such the book will be interesting in its own right. The most important features of the book, however, will be the thorough description of the various attempts of hypercomputation: from trial-and-error machines to the exploration of the human mind, if we treat it as a computing device.
Computation And Its Limits
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Author : Paul Cockshott
language : en
Publisher: OUP Oxford
Release Date : 2012-03-15
Computation And Its Limits written by Paul Cockshott and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-15 with Science categories.
Computation and its Limits is an innovative cross-disciplinary investigation of the relationship between computing and physical reality. It begins by exploring the mystery of why mathematics is so effective in science and seeks to explain this in terms of the modelling of one part of physical reality by another. Going from the origins of counting to the most blue-skies proposals for novel methods of computation, the authors investigate the extent to which the laws of nature and of logic constrain what we can compute. In the process they examine formal computability, the thermodynamics of computation, and the promise of quantum computing.
The Singularity Is Near
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Author : Ray Kurzweil
language : en
Publisher: Penguin
Release Date : 2005-09-22
The Singularity Is Near written by Ray Kurzweil and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-22 with Social Science categories.
NEW YORK TIMES BESTSELLER • Celebrated futurist Ray Kurzweil, hailed by Bill Gates as “the best person I know at predicting the future of artificial intelligence,” presents an “elaborate, smart, and persuasive” (The Boston Globe) view of the future course of human development. “Artfully envisions a breathtakingly better world.”—Los Angeles Times “Startling in scope and bravado.”—Janet Maslin, The New York Times “An important book.”—The Philadelphia Inquirer At the onset of the twenty-first century, humanity stands on the verge of the most transforming and thrilling period in its history. It will be an era in which the very nature of what it means to be human will be both enriched and challenged as our species breaks the shackles of its genetic legacy and achieves inconceivable heights of intelligence, material progress, and longevity. While the social and philosophical ramifications of these changes will be profound, and the threats they pose considerable, The Singularity Is Near presents a radical and optimistic view of the coming age that is both a dramatic culmination of centuries of technological ingenuity and a genuinely inspiring vision of our ultimate destiny.
Limits To Parallel Computation
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Author : Raymond Greenlaw
language : en
Publisher:
Release Date : 1995
Limits To Parallel Computation written by Raymond Greenlaw and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.
This book provides a comprehensive analysis of the most important topics in parallel computation. It is written so that it may be used as a self-study guide to the field, and researchers in parallel computing will find it a useful reference for many years to come. The first half of the book consists of an introduction to many fundamental issues in parallel computing. The second half provides lists of P-complete- and open problems. These lists will have lasting value to researchers in both industry and academia. The lists of problems, with their corresponding remarks, the thorough index, and the hundreds of references add to the exceptional value of this resource. While the exciting field of parallel computation continues to expand rapidly, this book serves as a guide to research done through 1994 and also describes the fundamental concepts that new workers will need to know in coming years. It is intended for anyone interested in parallel computing, including senior level undergraduate students, graduate students, faculty, and people in industry. As an essential reference, the book will be needed in all academic libraries.
Feynman And Computation
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Author : Anthony Hey
language : en
Publisher: CRC Press
Release Date : 2018-03-08
Feynman And Computation written by Anthony Hey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Science categories.
Computational properties of use to biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
Computational Complexity
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Author : Sanjeev Arora
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20
Computational Complexity written by Sanjeev Arora 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 2009-04-20 with Computers categories.
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
What Can Be Computed
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Author : John MacCormick
language : en
Publisher: Princeton University Press
Release Date : 2018-05-01
What Can Be Computed written by John MacCormick and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-01 with Computers categories.
An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com
Computers Ltd
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Author : David Harel
language : en
Publisher: Oxford University Press
Release Date : 2004
Computers Ltd written by David Harel and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
The computer has been hailed as the greatest innovation of the 20th century, and there is no denying that these technological marvels have dramatically changed our everyday lives. They can fly airplanes and spaceships, route millions of phone calls simultaneously, and play chess with the world's greatest players. But how limitless is the future for the computer? Will computers one day be truly intelligent, make medical diagnoses, run companies, compose music, and fall in love? In Computers Ltd., David Harel, the best-selling author of Algorithmics, illuminates one of the most fundamental yet under-reported facets of computers--their inherent limitations. Looking only at the bad news that is proven, discussing limitations that no amounts of hardware, software, talent, or resources can overcome, the book presents a disturbing and provocative view of computing at the start of the 21st century. Harel takes us on a fascinating tour that touches on everything from tiling problems and monkey puzzles to Monte Carlo algorithms and quantum computing, showing just how far from perfect computers are, while shattering some of the many claims made for these machines. He concludes that though we may strive for bigger and better things in computing, we need to be realistic: computers are not omnipotent--far from it. Their limits are real and here to stay. Based on hard facts, mathematically proven and indisputable, Computers Ltd. offers a vividly written and often amusing look at the shape of the future.
The Amazing World Of Quantum Computing
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Author : Rajendra K. Bera
language : en
Publisher: Springer Nature
Release Date : 2020-03-14
The Amazing World Of Quantum Computing written by Rajendra K. Bera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-14 with Science categories.
This book discusses the application of quantum mechanics to computing. It explains the fundamental concepts of quantum mechanics and then goes on to discuss various elements of mathematics required for quantum computing. Quantum cryptography, waves and Fourier analysis, measuring quantum systems, comparison to classical mechanics, quantum gates, and important algorithms in quantum computing are among the topics covered. The book offers a valuable resource for graduate and senior undergraduate students in STEM (science, technology, engineering, and mathematics) fields with an interest in designing quantum algorithms. Readers are expected to have a firm grasp of linear algebra and some familiarity with Fourier analysis.