Limits Of Computation

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Limits of Computation

Author : Edna E. Reiter
Publisher : CRC Press
ISBN 13 : 143988207X
Total Pages : 279 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Limits of Computation by : Edna E. Reiter

Download or read book Limits of Computation written by Edna E. Reiter and published by CRC Press. This book was released on 2012-10-29 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limits of Computation: An Introduction to the Undecidable and the Intractable offers a gentle introduction to the theory of computational complexity. It explains the difficulties of computation, addressing problems that have no algorithm at all and problems that cannot be solved efficiently. The book enables readers to understand: What does it mean for a problem to be unsolvable or to be NP-complete? What is meant by a computation and what is a general model of a computer? What does it mean for an algorithm to exist and what kinds of problems have no algorithm? What problems have algorithms but the algorithm may take centuries to finish? Developed from the authors’ course on computational complexity theory, the text is suitable for advanced undergraduate and beginning graduate students without a strong background in theoretical computer science. Each chapter presents the fundamentals, examples, complete proofs of theorems, and a wide range of exercises.

Computation and Its Limits

Author : Paul Cockshott
Publisher : Oxford University Press
ISBN 13 : 0199640327
Total Pages : 246 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Computation and Its Limits by : Paul Cockshott

Download or read book Computation and Its Limits written by Paul Cockshott and published by Oxford University Press. This book was released on 2012-03-15 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although we are entirely unaware of it, computation is central to all aspects of our existences. Every day we solve, or try to solve, a myriad of problems, from the utterly trivial to the bafflingly complex. This book explains why it is possible to do computation and what the ultimate limits of it are, as understood by modern science.

Limits of Computation

Author : Bernhard Reus
Publisher : Springer
ISBN 13 : 3319278894
Total Pages : 348 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Limits of Computation by : Bernhard Reus

Download or read book Limits of Computation written by Bernhard Reus and published by Springer. This book was released on 2016-03-25 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook discusses the most fundamental and puzzling questions about the foundations of computing. In 23 lecture-sized chapters it provides an exciting tour through the most important results in the field of computability and time complexity, including the Halting Problem, Rice's Theorem, Kleene's Recursion Theorem, the Church-Turing Thesis, Hierarchy Theorems, and Cook-Levin's Theorem. Each chapter contains classroom-tested material, including examples and exercises. Links between adjacent chapters provide a coherent narrative. Fundamental results are explained lucidly by means of programs written in a simple, high-level imperative programming language, which only requires basic mathematical knowledge. Throughout the book, the impact of the presented results on the entire field of computer science is emphasised. Examples range from program analysis to networking, from database programming to popular games and puzzles. Numerous biographical footnotes about the famous scientists who developed the subject are also included. "Limits of Computation" offers a thorough, yet accessible, introduction to computability and complexity for the computer science student of the 21st century.

Limits to Parallel Computation

Author : Raymond Greenlaw
Publisher : Oxford University Press, USA
ISBN 13 : 0195085914
Total Pages : 328 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Limits to Parallel Computation by : Raymond Greenlaw

Download or read book Limits to Parallel Computation written by Raymond Greenlaw and published by Oxford University Press, USA. This book was released on 1995 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Energy Limits in Computation

Author : Craig S. Lent
Publisher : Springer
ISBN 13 : 3319934589
Total Pages : 237 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Energy Limits in Computation by : Craig S. Lent

Download or read book Energy Limits in Computation written by Craig S. Lent and published by Springer. This book was released on 2018-08-03 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a single-source reference to the issues involved in the Landauer principle, which has gained new prominence recently, due to the large amount of heat generated by today’s computers. If Landauer’s principle is correct, there may be ways to build computers that dissipate far less power (corresponding to heat generated) than today’s computers. This book brings together all sides of the discussions regarding Landauer’s principle, both theoretical and experimental, empowering readers to gain better understanding of dissipation in computation, and the limits if any to progress in computation related to energy dissipation. It represents the best and most thorough examination of the important issue of Landauer’s principle that is available in one volume. Provides an in-depth investigation of the Landauer principle and how it relates to the possible existence of lower bounds on dissipation in computation; Gathers together both sides of the discussion: those who agree with Landauer and his conclusions, and those who think that Landauer was not correct, offering fresh perspective on the issues in the new light of experiments; Offers insight into the future of silicon CMOS and the limits if any to progress in computation related to energy dissipation.

Feynman And Computation

Author : Anthony Hey
Publisher : CRC Press
ISBN 13 : 0429969007
Total Pages : 463 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Feynman And Computation by : Anthony Hey

Download or read book Feynman And Computation written by Anthony Hey and published by CRC Press. This book was released on 2018-03-08 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

In Pursuit of the Traveling Salesman

Author : William J. Cook
Publisher : Princeton University Press
ISBN 13 : 0691163529
Total Pages : 244 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis In Pursuit of the Traveling Salesman by : William J. Cook

Download or read book In Pursuit of the Traveling Salesman written by William J. Cook and published by Princeton University Press. This book was released on 2014-11-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The story of one of the greatest unsolved problems in mathematics What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics—and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today’s state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets. In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

Neural Networks and Analog Computation

Author : Hava T. Siegelmann
Publisher : Springer Science & Business Media
ISBN 13 : 146120707X
Total Pages : 193 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Neural Networks and Analog Computation by : Hava T. Siegelmann

Download or read book Neural Networks and Analog Computation written by Hava T. Siegelmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theoretical foundations of Neural Networks and Analog Computation conceptualize neural networks as a particular type of computer consisting of multiple assemblies of basic processors interconnected in an intricate structure. Examining these networks under various resource constraints reveals a continuum of computational devices, several of which coincide with well-known classical models. On a mathematical level, the treatment of neural computations enriches the theory of computation but also explicated the computational complexity associated with biological networks, adaptive engineering tools, and related models from the fields of control theory and nonlinear dynamics. The material in this book will be of interest to researchers in a variety of engineering and applied sciences disciplines. In addition, the work may provide the base of a graduate-level seminar in neural networks for computer science students.

Self-Organizing Systems, 1962

Author : Marshall C. Yovits
Publisher :
ISBN 13 : 9781258715038
Total Pages : 574 pages
Book Rating : 4.7/5 (15 download)

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Book Synopsis Self-Organizing Systems, 1962 by : Marshall C. Yovits

Download or read book Self-Organizing Systems, 1962 written by Marshall C. Yovits and published by . This book was released on 2013-05 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributing Authors Include O. G. Selfridge, Mihajlo D. Mesarovic, D. M. Mackay And Others.

Formal Models of Computation

Author : Arthur Fleck
Publisher : World Scientific Publishing Company
ISBN 13 : 9813105828
Total Pages : 548 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Formal Models of Computation by : Arthur Fleck

Download or read book Formal Models of Computation written by Arthur Fleck and published by World Scientific Publishing Company. This book was released on 2001-03-09 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides new presentations of standard computational models that help avoid pitfalls of the conventional description methods. It also includes novel approaches to some of the topics that students normally find the most challenging. The presentations have evolved in response to student feedback over many years of teaching and have been well received by students. The book covers the topics suggested in the ACM curriculum guidelines for the course on “Theory of Computation”, and in the course on “Foundations of Computing” in the model liberal arts curriculum. These are standard courses for upper level computer science majors and beginning graduate students. The material in this area of computing is intellectually deep, and students invariably find it challenging to master. This book blends the three key ingredients for successful mastery. The first is its focus on the mingling of intuition and rigor that is required to fully understand the area. This is accomplished not only in the discussion and in examples, but also especially in the proofs. Second, a number of practical applications are presented to illustrate the capacity of the theoretical techniques to contribute insights in a variety of areas; such presentations greatly increase the reader's motivation to grasp the theoretical material. The student's active participation is the third and final major element in the learning process, and to this end an extensive collection of problems of widely differing difficulty is incorporated.

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: 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

What Can Be Computed?

Author : John MacCormick
Publisher : Princeton University Press
ISBN 13 : 0691170665
Total Pages : 404 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis What Can Be Computed? by : John MacCormick

Download or read book What Can Be Computed? written by John MacCormick and published by Princeton University Press. This book was released on 2018-05-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Amazing World of Quantum Computing

Author : Rajendra K. Bera
Publisher : Springer Nature
ISBN 13 : 9811524718
Total Pages : 278 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis The Amazing World of Quantum Computing by : Rajendra K. Bera

Download or read book The Amazing World of Quantum Computing written by Rajendra K. Bera and published by Springer Nature. This book was released on 2020-03-14 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Information, Physics, and Computation

Author : Marc Mézard
Publisher : Oxford University Press
ISBN 13 : 019857083X
Total Pages : 584 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Information, Physics, and Computation by : Marc Mézard

Download or read book Information, Physics, and Computation written by Marc Mézard and published by Oxford University Press. This book was released on 2009-01-22 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Computation and its Limits

Author : Paul Cockshott
Publisher : OUP Oxford
ISBN 13 : 0191627496
Total Pages : 248 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Computation and its Limits by : Paul Cockshott

Download or read book Computation and its Limits written by Paul Cockshott and published by OUP Oxford. This book was released on 2012-03-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Computing

Author : National Academies of Sciences, Engineering, and Medicine
Publisher : National Academies Press
ISBN 13 : 030947969X
Total Pages : 273 pages
Book Rating : 4.3/5 (94 download)

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Book Synopsis Quantum Computing by : National Academies of Sciences, Engineering, and Medicine

Download or read book Quantum Computing written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2019-04-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

Limits, Series, and Fractional Part Integrals

Author : Ovidiu Furdui
Publisher : Springer Science & Business Media
ISBN 13 : 1461467624
Total Pages : 289 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Limits, Series, and Fractional Part Integrals by : Ovidiu Furdui

Download or read book Limits, Series, and Fractional Part Integrals written by Ovidiu Furdui and published by Springer Science & Business Media. This book was released on 2013-05-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features challenging problems of classical analysis that invite the reader to explore a host of strategies and tools used for solving problems of modern topics in real analysis. This volume offers an unusual collection of problems — many of them original — specializing in three topics of mathematical analysis: limits, series, and fractional part integrals. The work is divided into three parts, each containing a chapter dealing with a particular problem type as well as a very short section of hints to select problems. The first chapter collects problems on limits of special sequences and Riemann integrals; the second chapter focuses on the calculation of fractional part integrals with a special section called ‘Quickies’ which contains problems that have had unexpected succinct solutions. The final chapter offers the reader an assortment of problems with a flavor towards the computational aspects of infinite series and special products, many of which are new to the literature. Each chapter contains a section of difficult problems which are motivated by other problems in the book. These ‘Open Problems’ may be considered research projects for students who are studying advanced calculus, and which are intended to stimulate creativity and the discovery of new and original methods for proving known results and establishing new ones. This stimulating collection of problems is intended for undergraduate students with a strong background in analysis; graduate students in mathematics, physics, and engineering; researchers; and anyone who works on topics at the crossroad between pure and applied mathematics. Moreover, the level of problems is appropriate for students involved in the Putnam competition and other high level mathematical contests.