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Parallel pattern generation with one-way communications

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Results and Trends in Theoretical Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 812))

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Abstract

We study (static) patterns generated by Cellular Automata (CA). In particular, we consider CA with one-dimensional information flow (for each axis of coordinates) called one-way CA and CA with information flow only away from the center of coordinates, called one-way rooted CA. For example, we show that any pattern that can be generated by a one-way CA can be generated in linear time. The converse holds in the one-dimensional case. We show an interesting connection between patterns generated by CA, fixed points of CA and tilings of Euclidean spaces. We show that it is undecidable whether a CA converges to a pattern from a given finite configuration or from any configuration.

Supported by the National Science Foundation under Grant No. CCR-9202396

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References

  1. K. Culik II, How to Fire Almost any Pattern on Cellular Automaton. In “Cellular Automata and Cooperative Systems”. Boccara, Goles, Martinez, Picco (Eds.), Kluwer Academic Publishers, the Netherlands, 101–109, 1993.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of South Carolina, 29208, Columbia, S.C.

    Karel Culik II

  2. Mathematics Department, University of Turku, 20500, Turku, Finland

    Jarkko Kari

Authors
  1. Karel Culik II
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  2. Jarkko Kari
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Juliani Karhumäki Hermann Maurer Grzegorz Rozenberg

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© 1994 Springer-Verlag Berlin Heidelberg

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Culik, K., Kari, J. (1994). Parallel pattern generation with one-way communications. In: Karhumäki, J., Maurer, H., Rozenberg, G. (eds) Results and Trends in Theoretical Computer Science. Lecture Notes in Computer Science, vol 812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58131-6_39

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  • DOI: https://doi.org/10.1007/3-540-58131-6_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58131-4

  • Online ISBN: 978-3-540-48445-5

  • eBook Packages: Springer Book Archive

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