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On Some Topological Properties of Linear Cellular Automata

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Mathematical Foundations of Computer Science 1999 (MFCS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1672))

Abstract

We study two dynamical properties of linear. D-dimensional cellular automata over Zm namely, denseness of periodic points and topological mixing. For what concerns denseness of periodic points, we complete the work initiated in [9], [3], and [2] by proving that a linear cellular automata has dense periodic points over the entire space of configurations if and only if it is surjective (as conjectured in [2]). For non-surjective linear CA we give a complete characterization of the subspace where periodic points are dense. For what concerns topological mixing, we prove that this property is equivalent to transitivity and then easily checkable. Finally, we classify linear cellular automata according to the definition of chaos given by Devaney in [8].

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References

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Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università di Bologna, Mura Anteo Zamboni 7, 40127, Bologna, Italy

    Luciano Margara

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  1. Luciano Margara
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Editors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Przesmyckiego 20, PL-51-151, Wrocław, Poland

    Mirosław Kutyłowski , Leszek Pacholski  & Tomasz Wierzbicki ,  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Margara, L. (1999). On Some Topological Properties of Linear Cellular Automata. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_19

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  • DOI: https://doi.org/10.1007/3-540-48340-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66408-6

  • Online ISBN: 978-3-540-48340-3

  • eBook Packages: Springer Book Archive

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