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Cellular Automata Probability Measures

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Cellular Automata and Modeling of Complex Physical Systems

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 46))

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Abstract

The finite time probability measures of a one-dimensional cellular automaton are characterized using stochastic finite automata, which provides an analogy for probability measures to the theorem by Wolfram stating that the finite time sets are regular languages. The exact time evolution of the probability measure and the evolution of quantities measuring randomness and complexity are calculated in some examples. We also introduce a new approximation scheme for the time evolution of the probability measure.

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Author information

Authors and Affiliations

  1. NORDITA, Blegdamsvej 17, DK-2100, Copenhagen, Denmark

    M. G. Nordahl

Authors
  1. M. G. Nordahl
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Editor information

Editors and Affiliations

  1. Service de Physique du Solide et de Résonance Magnétique, Centre d’Etudes Nucléaires de Saclay, Institut de Recherche Fondamentale, F-91191, Gif-sur-Yvette Cedex, France

    Paul Manneville  & Roger Bidaux  & 

  2. Centre de Physique, Université Scientifique et Médicale, F-74310, Les Houches, France

    Nino Boccara

  3. Plasma Fusion Center, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Gérard Y. Vichniac

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© 1989 Springer-Verlag Berlin Heidelberg

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Nordahl, M.G. (1989). Cellular Automata Probability Measures. In: Manneville, P., Boccara, N., Vichniac, G.Y., Bidaux, R. (eds) Cellular Automata and Modeling of Complex Physical Systems. Springer Proceedings in Physics, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75259-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-75259-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-75261-2

  • Online ISBN: 978-3-642-75259-9

  • eBook Packages: Springer Book Archive

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