Understanding Computation

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

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.

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

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.

Computation and Storage in the Cloud is the first comprehensive and systematic work investigating the issue of computation and storage trade-off in the cloud in order to reduce the overall application cost. Scientific applications are usually computation and data intensive, where complex computation tasks take a long time for execution and the generated datasets are often terabytes or petabytes in size. Storing valuable generated application datasets can save their regeneration cost when they are reused, not to mention the waiting time caused by regeneration. However, the large size of the scientific datasets is a big challenge for their storage. By proposing innovative concepts, theorems and algorithms, this book will help bring the cost down dramatically for both cloud users and service providers to run computation and data intensive scientific applications in the cloud. Covers cost models and benchmarking that explain the necessary tradeoffs for both cloud providers and users Describes several novel strategies for storing application datasets in the cloud Includes real-world case studies of scientific research applications Covers cost models and benchmarking that explain the necessary tradeoffs for both cloud providers and users Describes several novel strategies for storing application datasets in the cloud Includes real-world case studies of scientific research applications

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

“The Language of Design” articulates the theory that there is a language of design. Drawing upon insights from computational language processing, the language of design is modeled computationally through latent semantic analysis (LSA), lexical chain analysis (LCA), and sentiment analysis (SA). The statistical co-occurrence of semantics (LSA), semantic relations (LCA), and semantic modifiers (SA) in design text is used to illustrate how the reality producing effect of language is itself an enactment of design, allowing a new understanding of the connections between creative behaviors. The computation of the language of design makes it possible to make direct measurements of creative behaviors which are distributed across social spaces and mediated through language. The book demonstrates how machine understanding of design texts based on computation over the language of design yields practical applications for design management.

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 functional programming and lambda calculus. It’s ideal for programmers versed in modern languages, with little or no formal training in computer science. Discover the theoretical underpinnings of your work with Understanding Computation. Learn fundamental computing concepts, such as Turing equivalence in languages Discover how programs can handle difficult or impossible problems Explore how many features a programming language needs Examine how computers can help you write correct programs Understand how to build data structures without mutation of state Learn how programmers can make a simple language like the lambda calculus actually run on a computer