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Abstract Geometrical Computation: Turing-Computing Ability and Undecidability

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New Computational Paradigms (CiE 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3526))

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Abstract

In the Cellular Automata (CA) literature, discrete lines inside (discrete) space-time diagrams are often idealized as Euclidean lines in order to analyze a dynamics or to design CA for special purposes. In this article, we present a parallel analog model of computation corresponding to this idealization: dimensionless signals are moving on a continuous space in continuous time generating Euclidean lines on (continuous) space-time diagrams. Like CA, this model is parallel, synchronous, uniform in space and time, and uses local updating. The main difference is that space and time are continuous and not discrete (ie ℝ instead of ℤ). In this article, the model is restricted to ℚ in order to remain inside Turing-computation theory. We prove that our model can carry out any Turing-computation through two-counter automata simulation and provide some undecidability results.

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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, France

    Jérôme Durand-Lose

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  1. Jérôme Durand-Lose
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Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  2. Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Benedikt Löwe

  3. Universiteit van Amsterdam,  

    Leen Torenvliet

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© 2005 Springer-Verlag Berlin Heidelberg

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Durand-Lose, J. (2005). Abstract Geometrical Computation: Turing-Computing Ability and Undecidability. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_14

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  • DOI: https://doi.org/10.1007/11494645_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26179-7

  • Online ISBN: 978-3-540-32266-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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