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On ergodic linear cellular automata over Zm

  • Parallel and Distributed Systems II
  • Conference paper
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STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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Abstract

We study the ergodic behavior of linear cellular automata over Zm. The main contribution of this paper is an easy-to-check necessary and sufficient condition for a linear cellular automaton over Zm to be ergodic. We prove that, for general cellular automata, ergodicity is equivalent to topological chaos (transitivity and sensitivity to initial conditions). Finally we prove that linear CA over Zp with p prime have dense periodic orbits.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell'Informazione, Università di Milano, Milano, Italy

    Gianpiero Cattaneo & Enrico Formenti

  2. Dipartimento di Scienze e Tecnologie Avanzate, Università di Torino, Via Cavour 84, 15100, Alessandria, Italy

    Giovanni Manzini

  3. Istituto di Matematica Computazionale, Via S. Maria, 46, 56126, Pisa, Italy

    Giovanni Manzini

  4. Dipartimento Scienze dell'Informazione, Università di Bologna, Piazza Porta S. Donato 5, 40127, Bologna, Italy

    Luciano Margara

Authors
  1. Gianpiero Cattaneo
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  2. Enrico Formenti
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  3. Giovanni Manzini
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  4. Luciano Margara
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Editor information

Rüdiger Reischuk Michel Morvan

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© 1997 Springer-Verlag Berlin Heidelberg

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Cattaneo, G., Formenti, E., Manzini, G., Margara, L. (1997). On ergodic linear cellular automata over Zm . In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023478

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  • DOI: https://doi.org/10.1007/BFb0023478

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

  • eBook Packages: Springer Book Archive

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