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Periodicity and Transitivity for Cellular Automata in Besicovitch Topologies

  • F. Blanchard
  • J. Cervelle
  • E. Formenti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)

Abstract

We study cellular automata (CA) behavior in Besicovitch topology. We solve an open problem about the existence of transitive CA. The proof of this result has some interest in its own since it is obtained by using Kolmogorov complexity. At our knowledge it if the first result on discrete dynamical systems obtained using Kolmogorov complexity. We also prove that every CA (in Besicovitch topology) either has a unique fixed point or a countable set of periodic points. This result underlines that CA have a great degree of stability and may be considered a further step towards the understanding of CA periodic behavior.

Keywords

Cellular Automaton Periodic Point Cellular Automaton Local Rule Kolmogorov Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • F. Blanchard
    • 1
  • J. Cervelle
    • 2
  • E. Formenti
    • 3
  1. 1.Institut de Mathématique de LuminyCNRSMarseille Cedex 9France
  2. 2.Laboratoire d’informatique Institut Gaspard-MongeMarne-la-Vallée Cedex 2France
  3. 3.Laboratoire d’Informatique Fondamentale de Marseille (LIF)Marseille Cedex 13France

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