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Computation: Finite and Infinite Machines

TL;DR: In this article, the authors present an abstract theory that categorically and systematically describes what all these machines can do and what they cannot do, giving sound theoretical or practical grounds for each judgment, and the abstract theory tells us in no uncertain terms that the machines' potential range is enormous and that its theoretical limitations are of the subtlest and most elusive sort.
Abstract: From the Preface (See Front Matter for full Preface) Man has within a single generation found himself sharing the world with a strange new species: the computers and computer-like machines. Neither history, nor philosophy, nor common sense will tell us how these machines will affect us, for they do not do "work" as did machines of the Industrial Revolution. Instead of dealing with materials or energy, we are told that they handle "control" and "information" and even "intellectual processes." There are very few individuals today who doubt that the computer and its relatives are developing rapidly in capability and complexity, and that these machines are destined to play important (though not as yet fully understood) roles in society's future. Though only some of us deal directly with computers, all of us are falling under the shadow of their ever-growing sphere of influence, and thus we all need to understand their capabilities and their limitations. It would indeed be reassuring to have a book that categorically and systematically described what all these machines can do and what they cannot do, giving sound theoretical or practical grounds for each judgment. However, although some books have purported to do this, it cannot be done for the following reasons: a) Computer-like devices are utterly unlike anything which science has ever considered---we still lack the tools necessary to fully analyze, synthesize, or even think about them; and b) The methods discovered so far are effective in certain areas, but are developing much too rapidly to allow a useful interpretation and interpolation of results. The abstract theory---as described in this book---tells us in no uncertain terms that the machines' potential range is enormous, and that its theoretical limitations are of the subtlest and most elusive sort. There is no reason to suppose machines have any limitations not shared by man.
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Book
01 Jan 1974
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Abstract: From the Publisher: With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter. 0201000296B04062001

9,262 citations

Journal ArticleDOI
TL;DR: The model provides a unifying view of all systems that restrict information flow, enables a classification of them according to security objectives, and suggests some new approaches to formulating the requirements of secure information flow among security classes.
Abstract: This paper investigates mechanisms that guarantee secure information flow in a computer system. These mechanisms are examined within a mathematical framework suitable for formulating the requirements of secure information flow among security classes. The central component of the model is a lattice structure derived from the security classes and justified by the semantics of information flow. The lattice properties permit concise formulations of the security requirements of different existing systems and facilitate the construction of mechanisms that enforce security. The model provides a unifying view of all systems that restrict information flow, enables a classification of them according to security objectives, and suggests some new approaches. It also leads to the construction of automatic program certification mechanisms for verifying the secure flow of information through a program.

1,943 citations

Journal ArticleDOI
TL;DR: Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.

1,692 citations

Alex Graves1, Greg Wayne1, Ivo Danihelka1
20 Oct 2014
TL;DR: A combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-toend, allowing it to be efficiently trained with gradient descent.
Abstract: We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-toend, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.

1,471 citations

Journal ArticleDOI
TL;DR: This paper analyzes the literature from the point of view of swarm engineering and proposes two taxonomies: in the first taxonomy, works that deal with design and analysis methods are classified; in the second, works according to the collective behavior studied are classified.
Abstract: Swarm robotics is an approach to collective robotics that takes inspiration from the self-organized behaviors of social animals. Through simple rules and local interactions, swarm robotics aims at designing robust, scalable, and flexible collective behaviors for the coordination of large numbers of robots. In this paper, we analyze the literature from the point of view of swarm engineering: we focus mainly on ideas and concepts that contribute to the advancement of swarm robotics as an engineering field and that could be relevant to tackle real-world applications. Swarm engineering is an emerging discipline that aims at defining systematic and well founded procedures for modeling, designing, realizing, verifying, validating, operating, and maintaining a swarm robotics system. We propose two taxonomies: in the first taxonomy, we classify works that deal with design and analysis methods; in the second taxonomy, we classify works according to the collective behavior studied. We conclude with a discussion of the current limits of swarm robotics as an engineering discipline and with suggestions for future research directions.

1,405 citations


Cites methods from "Computation: Finite and Infinite Ma..."

  • ...One of the most adopted design methods to obtain such behaviors is the use of a particular class of finite state machine (Minsky, 1967): probabilistic finite state machines (PFSMs)....

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  • ...One of the most adopted design methods to obtain such behaviors is the use of a particular class of finite state machine (Minsky 1967): probabilistic finite state machines (PFSMs)....

    [...]