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Two-States Bilinear Intrinsically Universal Cellular Automata

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Fundamentals of Computation Theory (FCT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2138))

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Abstract

Linear cellular automata have been studied in details using algebraic techniques [3]. The generalization to families of polynomial cellular automata seems natural. The following step of complexity consists of bilinear cellular automata which study has begun with the work of Bartlett and Garzon [2]. Thanks to bulking techniques [5], two-states bilinear intrinsically universal cellular automata are constructed. This result answers a question from Bartlett and Garzon [2] of 1995.

A longer version of this paper is available from the author, see [6]

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References

  1. J. Albert and K. Čulik II. A simple universal cellular automaton and its one-way and totalistic version. Complex Systems, 1(1):1–16, 1987.

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  2. R. Bartlett and M. Garzon. Bilinear cellular automata. Complex Systems, 9(6):455–476, 1995.

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  3. O. Martin, A. M. Odyzko, and S. Wolfram. Algebraic properties of cellular automata. Commun. Math. Phys., 93:219–258, 1993.

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  4. J. Mazoyer and I. Rapaport. Inducing an order on cellular automata by a grouping operation. Discrete Appl. Math., 218:177–196, 1999.

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  5. N. Ollinger. Toward an algorithmic classification of cellular automata dynamics. LIP RR2001-10, http://www.ens-lyon.fr/LIP, 2001.

  6. N. Ollinger. Two-states bilinear intrinsically universal cellular automata. LIP RR2001-11, http://www.ens-lyon.fr/LIP, 2001.

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Author information

Authors and Affiliations

  1. LIP, École Normale Supérieure de Lyon, 46, allée d’Italie, 69 364, Lyon Cedex 07, France

    Nicolas Ollinger

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  1. Nicolas Ollinger
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Editor information

Editors and Affiliations

  1. University of Latvia, Raiņa bulvaris 29, LV-1459, Riga, Latvia

    Rūsiņš Freivalds

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© 2001 Springer-Verlag Berlin Heidelberg

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Ollinger, N. (2001). Two-States Bilinear Intrinsically Universal Cellular Automata. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_41

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  • DOI: https://doi.org/10.1007/3-540-44669-9_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42487-1

  • Online ISBN: 978-3-540-44669-9

  • eBook Packages: Springer Book Archive

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