Understanding Computation PDF Download

Author: Tom Stuart
Publisher: "O'Reilly Media, Inc."
ISBN: 144933010X
Category : Computers
Languages : en
Pages : 332

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Book Description
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

Author: John V. Guttag
Publisher: MIT Press
ISBN: 0262529629
Category : Computers
Languages : en
Pages : 466

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Book Description
The new edition of an introductory text that teaches students the art of computational problem solving, covering topics ranging from simple algorithms to information visualization. This book introduces students with little or no prior programming experience to the art of computational problem solving using Python and various Python libraries, including PyLab. It provides students with skills that will enable them to make productive use of computational techniques, including some of the tools and techniques of data science for using computation to model and interpret data. The book is based on an MIT course (which became the most popular course offered through MIT's OpenCourseWare) and was developed for use not only in a conventional classroom but in in a massive open online course (MOOC). This new edition has been updated for Python 3, reorganized to make it easier to use for courses that cover only a subset of the material, and offers additional material including five new chapters. Students are introduced to Python and the basics of programming in the context of such computational concepts and techniques as exhaustive enumeration, bisection search, and efficient approximation algorithms. Although it covers such traditional topics as computational complexity and simple algorithms, the book focuses on a wide range of topics not found in most introductory texts, including information visualization, simulations to model randomness, computational techniques to understand data, and statistical techniques that inform (and misinform) as well as two related but relatively advanced topics: optimization problems and dynamic programming. This edition offers expanded material on statistics and machine learning and new chapters on Frequentist and Bayesian statistics.

Author: Hector Zenil
Publisher: World Scientific
ISBN: 9814447781
Category : Computers
Languages : en
Pages : 856

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Book Description
This volume, with a Foreword writer Sir Roger Penrose, discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation?How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays, representing a field that assumes information and computation to be key in understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's “Calculating Space” (the MIT translation), and a panel discussion transcription on the topic, featuring worldwide experts in quantum mechanics, physics, cognition, computation and algorithmic complexity. The volume is dedicated to the memory of Alan M Turing — the inventor of universal computation, on the 100th anniversary of his birth, and is part of the Turing Centenary celebrations. Contents:Foreword (R Penrose)PrefaceAcknowledgementsIntroducing the Computable Universe (H Zenil)Historical, Philosophical & Foundational Aspects of Computation:Origins of Digital Computing: Alan Turing, Charles Babbage, & Ada Lovelace (D Swade)Generating, Solving and the Mathematics of Homo Sapiens. E Post's Views on Computation (L De Mol)Machines (R Turner)Effectiveness (N Dershowitz & E Falkovich)Axioms for Computability: Do They Allow a Proof of Church's Thesis? (W Sieg)The Mathematician's Bias — and the Return to Embodied Computation (S B Cooper)Intuitionistic Mathematics and Realizability in the Physical World (A Bauer)What is Computation? Actor Model versus Turing's Model (C Hewitt)Computation in Nature & the Real World:Reaction Systems: A Natural Computing Approach to the Functioning of Living Cells (A Ehrenfeucht, J Kleijn, M Koutny & G Rozenberg)Bacteria, Turing Machines and Hyperbolic Cellular Automata (M Margenstern)Computation and Communication in Unorganized Systems (C Teuscher)The Many Forms of Amorphous Computational Systems (J Wiedermann)Computing on Rings (G J Martínez, A Adamatzky & H V McIntosh)Life as Evolving Software (G J Chaitin)Computability and Algorithmic Complexity in Economics (K V Velupillai & S Zambelli)Blueprint for a Hypercomputer (F A Doria)Computation & Physics & the Physics of Computation:Information-Theoretic Teleodynamics in Natural and Artificial Systems (A F Beavers & C D Harrison)Discrete Theoretical Processes (DTP) (E Fredkin)The Fastest Way of Computing All Universes (J Schmidhuber)The Subjective Computable Universe (M Hutter)What Is Ultimately Possible in Physics? (S Wolfram)Universality, Turing Incompleteness and Observers (K Sutner)Algorithmic Causal Sets for a Computational Spacetime (T Bolognesi)The Computable Universe Hypothesis (M P Szudzik)The Universe is Lawless or “Pantôn chrêmatôn metron anthrôpon einai” (C S Calude, F W Meyerstein & A Salomaa)Is Feasibility in Physics Limited by Fantasy Alone? (C S Calude & K Svozil)The Quantum, Computation & Information:What is Computation? (How) Does Nature Compute? (D Deutsch)The Universe as Quantum Computer (S Lloyd)Quantum Speedup and Temporal Inequalities for Sequential Actions (M Żukowski)The Contextual Computer (A Cabello)A Gödel-Turing Perspective on Quantum States Indistinguishable from Inside (T Breuer)When Humans Do Compute Quantum (P Zizzi)Open Discussion Section:Open Discussion on A Computable Universe (A Bauer, T Bolognesi, A Cabello, C S Calude, L De Mol, F Doria, E Fredkin, C Hewitt, M Hutter, M Margenstern, K Svozil, M Szudzik, C Teuscher, S Wolfram & H Zenil)Live Panel Discussion (transcription):What is Computation? (How) Does Nature Compute? (C S Calude, G J Chaitin, E Fredkin, A J Leggett, R de Ruyter, T Toffoli & S Wolfram)Zuse's Calculating Space:Calculating Space (Rechnender Raum) (K Zuse)Afterword to Konrad Zuse's Calculating Space (A German & H Zenil) Readership: Graduate students who are specialized researchers in computer science, information theory, quantum theory and modern philosophy and the general public who are interested in these subject areas. Keywords:Digital Physics;Computational Universe;Digital Philosophy;Reality Theories of the Universe;Models of the World;Thring Computation RandomnessKey Features:The authors are all prominent researchersNo competing titlesState-of-the-art collection of technical papers and non-technical essays

Author: Lenore Blum
Publisher: Springer Science & Business Media
ISBN: 1461207010
Category : Computers
Languages : en
Pages : 456

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Book Description
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.

Author: Gordana Dodig Crnkovic
Publisher: World Scientific
ISBN: 9814295477
Category : Computers
Languages : en
Pages : 530

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Book Description
This volume provides a cutting-edge view of the world's leading authorities in fields where information and computation play a central role.

Author: Arnold L. Rosenberg
Publisher: Springer Nature
ISBN: 3030583767
Category : Computers
Languages : en
Pages : 550

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Book Description
In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians. By means of lessons and exercises on “doing” mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.

Author: Philip Tetlow
Publisher: CRC Press
ISBN: 1317004841
Category : Business & Economics
Languages : en
Pages : 407

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Book Description
The World Wide Web is truly astounding. It has changed the way we interact, learn and innovate. It is the largest sociotechnical system humankind has created and is advancing at a pace that leaves most in awe. It is an unavoidable fact that the future of the world is now inextricably linked to the future of the Web. Almost every day it appears to change, to get better and increase its hold on us. For all this we are starting to see underlying stability emerge. The way that Web sites rank in terms of popularity, for example, appears to follow laws with which we are familiar. What is fascinating is that these laws were first discovered, not in fields like computer science or information technology, but in what we regard as more fundamental disciplines like biology, physics and mathematics. Consequently the Web, although synthetic at its surface, seems to be quite 'natural' deeper down, and one of the driving aims of the new field of Web Science is to discover how far down such ’naturalness’ goes. If the Web is natural to its core, that raises some fundamental questions. It forces us, for example, to ask if the central properties of the Web might be more elemental than the truths we cling to from our understandings of the physical world. In essence, it demands that we question the very nature of information. Understanding Information and Computation is about such questions and one possible route to potentially mind-blowing answers.

Author: John MacCormick
Publisher: Princeton University Press
ISBN: 0691170665
Category : Computers
Languages : en
Pages : 404

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Book Description
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: Alexei Yu. Kitaev
Publisher: American Mathematical Soc.
ISBN: 0821832298
Category : Computers
Languages : en
Pages : 274

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Book Description
An introduction to a rapidly developing topic: the theory of quantum computing. Following the basics of classical theory of computation, the book provides an exposition of quantum computation theory. In concluding sections, related topics, including parallel quantum computation, are discussed.

Author: Edith Subramanya
Publisher: Springer Nature
ISBN: 303101555X
Category : Computers
Languages : en
Pages : 105

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Book Description
Human computation is a new and evolving research area that centers around harnessing human intelligence to solve computational problems that are beyond the scope of existing Artificial Intelligence (AI) algorithms. With the growth of the Web, human computation systems can now leverage the abilities of an unprecedented number of people via the Web to perform complex computation. There are various genres of human computation applications that exist today. Games with a purpose (e.g., the ESP Game) specifically target online gamers who generate useful data (e.g., image tags) while playing an enjoyable game. Crowdsourcing marketplaces (e.g., Amazon Mechanical Turk) are human computation systems that coordinate workers to perform tasks in exchange for monetary rewards. In identity verification tasks, users perform computation in order to gain access to some online content; an example is reCAPTCHA, which leverages millions of users who solve CAPTCHAs every day to correct words in books that optical character recognition (OCR) programs fail to recognize with certainty. This book is aimed at achieving four goals: (1) defining human computation as a research area; (2) providing a comprehensive review of existing work; (3) drawing connections to a wide variety of disciplines, including AI, Machine Learning, HCI, Mechanism/Market Design and Psychology, and capturing their unique perspectives on the core research questions in human computation; and (4) suggesting promising research directions for the future. Table of Contents: Introduction / Human Computation Algorithms / Aggregating Outputs / Task Routing / Understanding Workers and Requesters / The Art of Asking Questions / The Future of Human Computation