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On Universality of Radius 1/2 Number-Conserving Cellular Automata

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Book cover Unconventional Computation (UC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6079))

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Abstract

A number-conserving cellular automaton (NCCA) is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modeling of the physical conservation laws of mass or energy. In this paper we show a construction method of radius 1/2 NCCAs. The local transition function is expressed via a single unary function which can be regarded as ‘flows’ of numbers. In spite of the strong constraint, we constructed radius 1/2 NCCAs that simulate any radius 1/2 cellular automata or any radius 1 NCCA. We also consider the state complexity of these non-splitting simulations (4n 2 + 2n + 1 and 8n 2 + 12n − 16, respectively). These results also imply existence of an intrinsically universal radius 1/2 NCCA.

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Author information

Authors and Affiliations

  1. Department of Information Engineering, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Katsunobu Imai & Artiom Alhazov

  2. Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academiei 5, Chişinău, MD-2028, Moldova

    Artiom Alhazov

Authors
  1. Katsunobu Imai
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  2. Artiom Alhazov
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Auckland, Science Centre, 38 Princes Street, 1142, Auckland, New Zealand

    Cristian S. Calude

  2. Graduate School of Information Science and Technology, Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-8656, Tokyo, Japan

    Masami Hagiya

  3. Graduate School of Engineering, Department of Information Engineering, Hiroshima University, 739-8527, Higashi-Hiroshima, Japan

    Kenichi Morita

  4. Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  5. Department of Computer Science and Department of Electronics, University of York, YO10 5DD, Heslington, York, UK

    Jon Timmis

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Imai, K., Alhazov, A. (2010). On Universality of Radius 1/2 Number-Conserving Cellular Automata. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds) Unconventional Computation. UC 2010. Lecture Notes in Computer Science, vol 6079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13523-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-13523-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13522-4

  • Online ISBN: 978-3-642-13523-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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