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International Conference on Machines, Computations, and Universality

MCU 2004: Machines, Computations, and Universality pp 176–187Cite as

Abstract Geometrical Computation for Black Hole Computation

(Extended Abstract)

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3354))

Abstract

The Black hole model of computation provides super-Turing computing power since it offers the possibility to decide in finite (observer’s) time any recursively enumerable (\(\mathcal{R.E.}\)) problem. In this paper, we provide a geometric model of computation, conservative abstract geometrical computation, that, although being based on rational numbers, has the same property: it can simulate any Turing machine and can decide any \(\mathcal{R.E.}\) problem through the creation of an accumulation. Finitely many signals can leave any accumulation, and it can be known whether anything leaves. This corresponds to a black hole effect.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique Fondamentale d’Orléans, Université d’Orléans, B.P. 6759, F-45067, ORLÉANS Cedex 2

    Jérôme Durand-Lose

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  1. Jérôme Durand-Lose
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Editors and Affiliations

  1. IUT de Metz, LITA, Université Paul Verlaine - Metz, EA 3097, UFR MIM, Île du Saulcy, 57045, Metz, Cédex, France

    Maurice Margenstern

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Durand-Lose, J. (2005). Abstract Geometrical Computation for Black Hole Computation. In: Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2004. Lecture Notes in Computer Science, vol 3354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31834-7_14

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  • DOI: https://doi.org/10.1007/978-3-540-31834-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25261-0

  • Online ISBN: 978-3-540-31834-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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