The Nature of Computation

by Cristopher Moore
The Nature of Computation
Author: Cristopher Moore
Publisher: OUP Oxford
Total Pages: 1498
Release: 2011-08-11
Genre: Science
ISBN: 0191620807
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Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

The Nature of Computation

by Cristopher Moore
The Nature of Computation
Author: Cristopher Moore
Publisher: OUP Oxford
Total Pages: 1004
Release: 2011-08-12
Genre: Science
ISBN: 0191552763
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Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

The Nature of Computation

by Cristopher Moore
The Nature of Computation
Author: Cristopher Moore
Publisher: Oxford University Press
Total Pages: 1004
Release: 2011-08-11
Genre: Computers
ISBN: 0199233217
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The boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. In this book the authors introduce the reader to the fundamental concepts of computational complexity and give in-depth explorations of the major interfaces between computer science and physics.

The Nature of Physical Computation

by Oron Shagrir
The Nature of Physical Computation
Author: Oron Shagrir
Publisher: Oxford University Press
Total Pages: 319
Release: 2022
Genre: Computers
ISBN: 0197552382
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Computing systems are ubiquitous in contemporary life. Even the brain is thought to be a computing system of sorts. But what does it mean to say that a given organ or system "computes"? What is it about laptops, smartphones, and nervous systems that they are deemed to compute - and why does itseldom occur to us to describe stomachs, hurricanes, rocks, or chairs that way? These questions are key to laying the conceptual foundations of computational sciences, including computer science and engineering, and the cognitive and neural sciences.Oron Shagrir here provides an extended argument for the semantic view of computation, which states that semantic properties are involved in the nature of computing systems. The first part of the book provides general background. Although different in scope, these chapters have a common theme-namely,that the linkage between the mathematical theory of computability and the notion of physical computation is weak. The second part of the book reviews existing non-semantic accounts of physical computation. Shagrir analyze three influential accounts in greater depth and argues that none of theseaccounts is satisfactory, but each of them highlights certain key features of physical computation that he eventually adopts in his own semantic account of physical computation - a view that rests on a phenomenon known as simultaneous implementation (or "indeterminacy of computation"). Shagrircompletes the characterization of his account of computation and highlights the distinctive feature of computational explanations.

Mathematics and Computation

by Avi Wigderson
Mathematics and Computation
Author: Avi Wigderson
Publisher: Princeton University Press
Total Pages: 434
Release: 2019-10-29
Genre: Computers
ISBN: 0691189137
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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

Physical Computation

by Gualtiero Piccinini
Physical Computation
Author: Gualtiero Piccinini
Publisher: Oxford University Press, USA
Total Pages: 324
Release: 2015
Genre: Computers
ISBN: 0199658854
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Computation permeates our world, but a satisfactory philosophical theory of what it is has been lacking. Gualtiero Piccinini presents a mechanistic account of what makes a physical system a computing system. He argues that computation does not entail representation or information-processing, although information-processing entails computation.

The Ecology of Computation

by Bernardo A. Huberman
The Ecology of Computation
Author: Bernardo A. Huberman
Publisher:
Total Pages: 358
Release: 1988
Genre: Computers
ISBN:
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Propelled by advances in software design and increasing connectivity, distributed computational systems are acquiring characteristics reminiscent of social and biological organizations. This volume is a collection of articles dealing with the nature, design and implementation of these open computational systems. Although varied in their approach and methodology, the articles are related by the goal of understanding and building computational ecologies. They are grouped in three major sections. The first deals with general issues underlying open systems, studies of computational ecologies, and their similarities with social organizations. The second part deals with actual implementations of distributed computation, and the third discusses the overriding problem of designing suitable languages for open systems. All the articles are highly interdisciplinary, emphasizing the application of ecological ideas, game theory, market mechanisms, and evolutionary biology in the study of open systems.

What Can Be Computed?

by John MacCormick
What Can Be Computed?
Author: John MacCormick
Publisher: Princeton University Press
Total Pages: 404
Release: 2018-05-01
Genre: Computers
ISBN: 0691170665
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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

An Introduction to Natural Computation

by Dana H. Ballard
An Introduction to Natural Computation
Author: Dana H. Ballard
Publisher: MIT Press
Total Pages: 338
Release: 1999-01-22
Genre: Psychology
ISBN: 9780262522588
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This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It is now clear that the brain is unlikely to be understood without recourse to computational theories. The theme of An Introduction to Natural Computation is that ideas from diverse areas such as neuroscience, information theory, and optimization theory have recently been extended in ways that make them useful for describing the brains programs. This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It stresses the broad spectrum of learning models—ranging from neural network learning through reinforcement learning to genetic learning—and situates the various models in their appropriate neural context. To write about models of the brain before the brain is fully understood is a delicate matter. Very detailed models of the neural circuitry risk losing track of the task the brain is trying to solve. At the other extreme, models that represent cognitive constructs can be so abstract that they lose all relationship to neurobiology. An Introduction to Natural Computation takes the middle ground and stresses the computational task while staying near the neurobiology.