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International Symposium on Mathematical Foundations of Computer Science

MFCS 2001: Mathematical Foundations of Computer Science 2001 pp 248–260Cite as

Algorithmic Information Theory and Cellular Automata Dynamics

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2136))

Abstract

We study the ability of discrete dynamical systems to transform/ generate randomness in cellular spaces. Thus, we endow the space of bi-infinite sequences by a metric inspired by information distance (defined in the context of Kolmogorov complexity or algorithmic information theory). We prove structural properties of this space (non-separability, completeness, perfectness and infinite topological dimension), which turn out to be useful to understand the transformation of information performed by dynamical systems evolving on it. Finally, we focus on cellular automata and prove a dichotomy theorem: continuous cellular automata are either equivalent to the identity or to a constant one. This means that they cannot produce any amount of randomness.

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Author information

Authors and Affiliations

  1. LIM - CMI, 39 rue Joliot-Curie, 13453, Marseille Cedex 13, France

    Julien Cervelle, Bruno Durand & Enrico Formenti

Authors
  1. Julien Cervelle
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  2. Bruno Durand
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  3. Enrico Formenti
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Editor information

Editors and Affiliations

  1. Mathematical Institute, AS CR, Žitná 25, 115 67, Praha 1, Czech Republic

    Jiří Sgall

  2. Faculty of Mathematics and Physics Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00, Praha 1, Czech Republic

    Aleš Pultr  & Petr Kolman  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Cervelle, J., Durand, B., Formenti, E. (2001). Algorithmic Information Theory and Cellular Automata Dynamics. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_22

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  • DOI: https://doi.org/10.1007/3-540-44683-4_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42496-3

  • Online ISBN: 978-3-540-44683-5

  • eBook Packages: Springer Book Archive

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