What Can Be Computed

What Can Be Computed Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of What Can Be Computed book. This book definitely worth reading, it is an incredibly well-written.

What Can Be Computed?

Author : John MacCormick
Publisher : Princeton University Press
Page : 404 pages
File Size : 42,6 Mb
Release : 2018-05-01
Category : Computers
ISBN : 9780691170664

Get Book

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

Understanding Computation

Author : Tom Stuart
Publisher : "O'Reilly Media, Inc."
Page : 332 pages
File Size : 41,9 Mb
Release : 2013-05-15
Category : Computers
ISBN : 9781449330101

Get Book

Understanding Computation by Tom Stuart Pdf

Finally, you can learn computation theory and programming language design in an engaging, practical way. Understanding Computation explains theoretical computer science in a context you’ll recognize, helping you appreciate why these ideas matter and how they can inform your day-to-day programming. Rather than use mathematical notation or an unfamiliar academic programming language like Haskell or Lisp, this book uses Ruby in a reductionist manner to present formal semantics, automata theory, and functional programming with the lambda calculus. It’s ideal for programmers versed in modern languages, with little or no formal training in computer science. Understand fundamental computing concepts, such as Turing completeness in languages Discover how programs use dynamic semantics to communicate ideas to machines Explore what a computer can do when reduced to its bare essentials Learn how universal Turing machines led to today’s general-purpose computers Perform complex calculations, using simple languages and cellular automata Determine which programming language features are essential for computation Examine how halting and self-referencing make some computing problems unsolvable Analyze programs by using abstract interpretation and type systems

Elements of Computation Theory

Author : Arindama Singh
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 54,9 Mb
Release : 2009-04-30
Category : Computers
ISBN : 9781848824973

Get Book

Elements of Computation Theory by Arindama Singh Pdf

The foundation of computer science is built upon the following questions: What is an algorithm? What can be computed and what cannot be computed? What does it mean for a function to be computable? How does computational power depend upon programming constructs? Which algorithms can be considered feasible? For more than 70 years, computer scientists are searching for answers to such qu- tions. Their ingenious techniques used in answering these questions form the theory of computation. Theory of computation deals with the most fundamental ideas of computer s- ence in an abstract but easily understood form. The notions and techniques employed are widely spread across various topics and are found in almost every branch of c- puter science. It has thus become more than a necessity to revisit the foundation, learn the techniques, and apply them with con?dence. Overview and Goals This book is about this solid, beautiful, and pervasive foundation of computer s- ence. It introduces the fundamental notions, models, techniques, and results that form the basic paradigms of computing. It gives an introduction to the concepts and mathematics that computer scientists of our day use to model, to argue about, and to predict the behavior of algorithms and computation. The topics chosen here have shown remarkable persistence over the years and are very much in current use.

Concise Guide to Computation Theory

Author : Akira Maruoka
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 55,6 Mb
Release : 2011-04-29
Category : Computers
ISBN : 9780857295354

Get Book

Concise Guide to Computation Theory by Akira Maruoka Pdf

This textbook presents a thorough foundation to the theory of computation. Combining intuitive descriptions and illustrations with rigorous arguments and detailed proofs for key topics, the logically structured discussion guides the reader through the core concepts of automata and languages, computability, and complexity of computation. Topics and features: presents a detailed introduction to the theory of computation, complete with concise explanations of the mathematical prerequisites; provides end-of-chapter problems with solutions, in addition to chapter-opening summaries and numerous examples and definitions throughout the text; draws upon the author’s extensive teaching experience and broad research interests; discusses finite automata, context-free languages, and pushdown automata; examines the concept, universality and limitations of the Turing machine; investigates computational complexity based on Turing machines and Boolean circuits, as well as the notion of NP-completeness.

Computational Complexity

Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 43,9 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264

Get Book

Computational Complexity by Sanjeev Arora,Boaz Barak Pdf

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Complexity and Real Computation

Author : Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461207016

Get Book

Complexity and Real Computation by Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale Pdf

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.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 41,7 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130

Get Book

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

Introduction to the Theory of Computation

Author : Michael Sipser
Publisher : Thomson/Course Technology
Page : 437 pages
File Size : 44,7 Mb
Release : 2006
Category : Computational complexity
ISBN : 0619217642

Get Book

Introduction to the Theory of Computation by Michael Sipser Pdf

"Intended as an upper-level undergraduate or introductory graduate text in computer science theory," this book lucidly covers the key concepts and theorems of the theory of computation. The presentation is remarkably clear; for example, the "proof idea," which offers the reader an intuitive feel for how the proof was constructed, accompanies many of the theorems and a proof. Introduction to the Theory of Computation covers the usual topics for this type of text plus it features a solid section on complexity theory--including an entire chapter on space complexity. The final chapter introduces more advanced topics, such as the discussion of complexity classes associated with probabilistic algorithms.

Turing's Vision

Author : Chris Bernhardt
Publisher : MIT Press
Page : 209 pages
File Size : 45,8 Mb
Release : 2016-05-13
Category : Computers
ISBN : 9780262034548

Get Book

Turing's Vision by Chris Bernhardt Pdf

In 1936, when he was just twenty-four years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, "The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory." Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer. In the paper, "On Computable Numbers, with an Application to the Entscheidungsproblem," Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.

Nine Algorithms That Changed the Future

Author : John MacCormick
Publisher : Princeton University Press
Page : 232 pages
File Size : 51,9 Mb
Release : 2020-09-15
Category : Computers
ISBN : 9780691209050

Get Book

Nine Algorithms That Changed the Future by John MacCormick Pdf

Nine revolutionary algorithms that power our computers and smartphones Every day, we use our computers to perform remarkable feats. A simple web search picks out a handful of relevant needles from the world's biggest haystack. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers, and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? John MacCormick answers this question in language anyone can understand, using vivid examples to explain the fundamental tricks behind nine computer algorithms that power our PCs, tablets, and smartphones.

The Nature of Computation

Author : Cristopher Moore,Stephan Mertens
Publisher : OUP Oxford
Page : 631 pages
File Size : 44,9 Mb
Release : 2011-08-11
Category : Science
ISBN : 9780191620805

Get Book

The Nature of Computation by Cristopher Moore,Stephan Mertens Pdf

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 Future Computed

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,6 Mb
Release : 2018
Category : Electronic
ISBN : OCLC:1020674183

Get Book

The Future Computed by Anonim Pdf

The Feeling of Life Itself

Author : Christof Koch
Publisher : MIT Press
Page : 277 pages
File Size : 44,8 Mb
Release : 2019-09-24
Category : Science
ISBN : 9780262042819

Get Book

The Feeling of Life Itself by Christof Koch Pdf

A thought-provoking argument that consciousness—more widespread than previously assumed—is the feeling of being alive, not a type of computation or a clever hack In The Feeling of Life Itself, Christof Koch offers a straightforward definition of consciousness as any subjective experience, from the most mundane to the most exalted—the feeling of being alive. Psychologists study which cognitive operations underpin a given conscious perception. Neuroscientists track the neural correlates of consciousness in the brain, the organ of the mind. But why the brain and not, say, the liver? How can the brain—three pounds of highly excitable matter, a piece of furniture in the universe, subject to the same laws of physics as any other piece—give rise to subjective experience? Koch argues that what is needed to answer these questions is a quantitative theory that starts with experience and proceeds to the brain. In The Feeling of Life Itself, Koch outlines such a theory, based on integrated information. Koch describes how the theory explains many facts about the neurology of consciousness and how it has been used to build a clinically useful consciousness meter. The theory predicts that many, and perhaps all, animals experience the sights and sounds of life; consciousness is much more widespread than conventionally assumed. Contrary to received wisdom, however, Koch argues that programmable computers will not have consciousness. Even a perfect software model of the brain is not conscious. Its simulation is fake consciousness. Consciousness is not a special type of computation—it is not a clever hack. Consciousness is about being.

Algorithms and Computation

Author : Prosenjit K. Bose,Pat Morin
Publisher : Springer
Page : 662 pages
File Size : 43,8 Mb
Release : 2003-08-02
Category : Mathematics
ISBN : 9783540361367

Get Book

Algorithms and Computation by Prosenjit K. Bose,Pat Morin Pdf

This book constitutes the refereed proceedings of the 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, held in Vancouver, BC, Canada in November 2002. The 54 revised full papers presented together with 3 invited contributions were carefully reviewed and selected from close to 160 submissions. The papers cover all relevant topics in algorithmics and computation, in particular computational geometry, algorithms and data structures, approximation algorithms, randomized algorithms, graph drawing and graph algorithms, combinatorial optimization, computational biology, computational finance, cryptography, and parallel and distributedd algorithms.

Information, Physics, and Computation

Author : Marc Mézard,Andrea Montanari
Publisher : Oxford University Press
Page : 584 pages
File Size : 42,5 Mb
Release : 2009-01-22
Category : Computers
ISBN : 9780198570837

Get Book

Information, Physics, and Computation by Marc Mézard,Andrea Montanari Pdf

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.