Beyond the universal Turing machine

Copeland, B. Jack; Sylvan, Richard

doi:10.1080/00048409912348801

Cited by 77 publications

(41 citation statements)

References 33 publications

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“…Turing machines can in principle approximate machines with continuous changes, but cannot implement them exactly. This argument may also be found in [60]. A continuous machine with non-linear feedback loops may be chaotic and impossible to approximate discretely, even over short time scales.…”

Section: Continuum As a Results Of Interaction Asynchronous Communicamentioning

confidence: 87%

Dynamics of Information as Natural Computation

Dodig-Crnković¹

2011

Information

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Processes considered rendering information dynamics have been studied, among others in: questions and answers, observations, communication, learning, belief revision, logical inference, game-theoretic interactions and computation. This article will put the computational approaches into a broader context of natural computation, where information dynamics is not only found in human communication and computational machinery but also in the entire nature. Information is understood as representing the world (reality as an informational web) for a cognizing agent, while information dynamics (information processing, computation) realizes physical laws through which all the changes of informational structures unfold. Computation as it appears in the natural world is more general than the human process of calculation modeled by the Turing machine. Natural computing is epitomized through the interactions of concurrent, in general asynchronous computational processes which are adequately represented by what Abramsky names "the second generation models of computation" [1] which we argue to be the most general representation of information dynamics.

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Section: Continuum As a Results Of Interaction Asynchronous Communicamentioning

confidence: 87%

Dynamics of Information as Natural Computation

Dodig-Crnković¹

2011

Information

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“…TMs can in principle approximate machines with continuous changes, but cannot implement them exactly. This argument may also be found in (Copeland & Sylvan 1999). A continuous machine with non-linear feedback loops may be chaotic and impossible to approximate discretely, even over short time scales.…”

Section: Introductionmentioning

confidence: 87%

Significance of Models of Computation, from Turing Model to Natural Computation

Dodig-Crnković

2011

Minds & Machines

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Abstract. The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and sub-symbolic information processing levels.Present account of models of computation highlights several topics of importance for the development of new understanding of computing and its role: natural computation and the relationship between the model and physical implementation, interactivity as fundamental for computational modelling of concurrent information processing systems such as living organisms and their networks, and the new developments in logic needed to support this generalized framework. Computing understood as information processing is closely related to natural sciences; it helps us recognize connections between sciences, and provides a unified approach for modeling and simulating of both living and non-living systems.

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“…He stated that Turing machines are closed systems that do not accept input while operating, whereas the brain continually receives input from the environment. Based on this observation, Copeland has proposed the coupled Turing machine which is connected to the environment via one or more input channels 13 . However, as Christof Teuscher and Moshe Sipper have pointed out 65 , any coupled machine with a finite f In his 1951 Gibbs lecture 22 Gödel attempts to use incompleteness to reason about human intelligence.…”

Section: Modeling the Brainmentioning

confidence: 99%

“…Based on several thoughts, some authors from very diverse research areas (Philosophy, Physics, Computer Science, etc.) claim that the human mind could be more powerful than Turing Machines 47,52,13,59 . Nevertheless, they do not agree on what these "super-Turing" capabilities mean.…”

Section: Introductionmentioning

confidence: 99%

On the Possible Computational Power of the Human Mind

Zenil

Hernández-Quiroz

2007

Worldviews, Science and Us

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The aim of this paper is to address the question: Can an artificial neural network (ANN) model be used as a possible characterization of the power of the human mind? We will discuss what might be the relationship between such a model and its natural counterpart. A possible characterization of the different power capabilities of the mind is suggested in terms of the information contained (in its computational complexity) or achievable by it. Such characterization takes advantage of recent results based on natural neural networks (NNN) and the computational power of arbitrary artificial neural networks (ANN). The possible acceptance of neural networks as the model of the human mind's operation makes the aforementioned quite relevant.

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Beyond the universal Turing machine

Cited by 77 publications

References 33 publications

Dynamics of Information as Natural Computation

Dynamics of Information as Natural Computation

Significance of Models of Computation, from Turing Model to Natural Computation

On the Possible Computational Power of the Human Mind

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