Limits Of Computation

Author : Bernhard Reus
Publisher : Springer
Page : 348 pages
File Size : 49,6 Mb
Release : 2016-03-25
Category : Computers
ISBN : 9783319278896

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Limits of Computation by Bernhard Reus Pdf

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.

Author : Edna E. Reiter,Clayton Matthew Johnson
Publisher : CRC Press
Page : 279 pages
File Size : 41,5 Mb
Release : 2012-10-29
Category : Computers
ISBN : 9781439882078

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Limits of Computation by Edna E. Reiter,Clayton Matthew Johnson Pdf

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.

Author : Paul Cockshott,Lewis M Mackenzie,Gregory Michaelson
Publisher : Oxford University Press
Page : 246 pages
File Size : 52,5 Mb
Release : 2012-03-15
Category : Computers
ISBN : 9780199640324

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Computation and Its Limits by Paul Cockshott,Lewis M Mackenzie,Gregory Michaelson Pdf

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.

Author : Craig S. Lent,Alexei O. Orlov,Wolfgang Porod,Gregory L. Snider
Publisher : Springer
Page : 237 pages
File Size : 40,8 Mb
Release : 2018-08-03
Category : Technology & Engineering
ISBN : 9783319934587

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Energy Limits in Computation by Craig S. Lent,Alexei O. Orlov,Wolfgang Porod,Gregory L. Snider Pdf

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.

Author : Anthony Hey
Publisher : CRC Press
Page : 463 pages
File Size : 52,6 Mb
Release : 2018-03-08
Category : Science
ISBN : 9780429969003

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Feynman And Computation by Anthony Hey Pdf

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.

Author : Raymond Greenlaw,H. James Hoover,Walter L. Ruzzo
Publisher : Oxford University Press, USA
Page : 328 pages
File Size : 41,8 Mb
Release : 1995
Category : Computational complexity
ISBN : 9780195085914

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Limits to Parallel Computation by Raymond Greenlaw,H. James Hoover,Walter L. Ruzzo Pdf

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.

Author : Hava T. Siegelmann
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461207078

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Neural Networks and Analog Computation by Hava T. Siegelmann Pdf

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.

Author : Arthur Fleck
Publisher : World Scientific Publishing Company
Page : 548 pages
File Size : 49,7 Mb
Release : 2001-03-09
Category : Computers
ISBN : 9789813105829

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Formal Models of Computation by Arthur Fleck Pdf

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.

Author : Paul Cockshott,Lewis M. Mackenzie,Gregory Michaelson
Publisher : OUP Oxford
Page : 248 pages
File Size : 55,8 Mb
Release : 2012-03-15
Category : Science
ISBN : 9780191627491

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Computation and its Limits by Paul Cockshott,Lewis M. Mackenzie,Gregory Michaelson Pdf

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.

Author : William J. Cook
Publisher : Princeton University Press
Page : 244 pages
File Size : 41,7 Mb
Release : 2014-11-09
Category : Mathematics
ISBN : 9780691163529

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In Pursuit of the Traveling Salesman by William J. Cook Pdf

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.

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 53,7 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130

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Mathematics and Computation by Avi Wigderson Pdf

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

Author : Anthony J.G. Hey
Publisher : Westview Press
Page : 472 pages
File Size : 53,9 Mb
Release : 1999
Category : Biography & Autobiography
ISBN : UOM:39015069323452

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Feynman And Computation by Anthony J.G. Hey Pdf

Richard P. Feynman made profoundly important contributions to the physics of computing, notably with such articles as "Simulating Physics with Computers", the famous paper which launched the field of quantum computing. This book offers both a remarkable tribute to Feynman and a new exploration of the limits of computers by some of today's most influential scientists.

Author : John MacCormick
Publisher : Princeton University Press
Page : 404 pages
File Size : 55,7 Mb
Release : 2018-05-01
Category : Computers
ISBN : 9780691170664

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What Can Be Computed? by John MacCormick Pdf

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

Author : Ovidiu Furdui
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 50,6 Mb
Release : 2013-05-30
Category : Mathematics
ISBN : 9781461467625

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Limits, Series, and Fractional Part Integrals by Ovidiu Furdui Pdf

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.

Author : Henry M. Walker
Publisher : Jones & Bartlett Publishers
Page : 236 pages
File Size : 55,8 Mb
Release : 1994
Category : Computers
ISBN : UVA:X002279956

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The Limits of Computing by Henry M. Walker Pdf