On Universality of Radius 1/2 Number-Conserving Cellular Automata | SpringerLink
Skip to main content
Springer Nature Link
Log in

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

  • Conference paper
Unconventional Computation (UC 2010)

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

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Boccara, N., Fukś, H.: Number-conserving cellular automaton rules. Fundamenta Informaticae 52, 1–13 (2003)

    Google Scholar 

  2. Durand, B., Formenti, E., Grange, A., Róka, Z.: Number conserving cellular automata: new results on decidability and dynamics. In: Morvan, M., Rémila, É. (eds.) Proceedings of Discrete Models for Complex Systems, DMCS 2003. Discrete Mathematics and Theoretical Computer Science, vol. AB, pp. 129–140 (2003)

    Google Scholar 

  3. Durand, B., Formenti, E., Róka, Z.: Number conserving cellular automata I: decidability. Theoretical Computer Science 299(1-3), 523–535 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fukś, H., Sullivan, K.: Enumeration of number-conserving cellular automata rules with two inputs. Journal of Cellular Automata 2(2), 141–148 (2007)

    MATH  MathSciNet  Google Scholar 

  5. Hattori, T., Takesue, S.: Additive conserved quantities in discrete-time lattice dynamical systems. Pysica 49D, 295–322 (1991)

    MathSciNet  Google Scholar 

  6. Imai, K., Fujita, K., Iwamoto, C., Morita, K.: Embedding a logically universal model and a self-reproducing model into number-conserving cellular automata. In: Calude, C.S., Dinneen, M.J., Peper, F. (eds.) UMC 2002. LNCS, vol. 2509, pp. 164–175. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Imai, K., Ikazaki, A., Iwamoto, C., Morita, K.: A logically universal number-conserving cellular automaton with a unary table-lookup function. Trans. IEICE E87-D(3), 694–699 (2004)

    Google Scholar 

  8. Kasai, Y.: Number-conserving cellular automata with universality under errors, Master’s thesis, Hiroshima University (2003)

    Google Scholar 

  9. Moreira, A.: Universality and decidability of number-conserving cellular automata. Theoretical Computer Science 292, 711–721 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Moreira, A., Boccara, N., Goles, E.: On conservative and monotone one-dimensional cellular automata and their particle representation. Theoretical Computer Science 325, 285–316 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Morita, K.: Computation-universality of one-dimensional one-way reversible cellular automata. Information Processing Letters 42, 325–329 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  12. Nagel, K., Schreckenberg, M.: A cellular automaton for freeway traffic. Journal of Physics I(2), 2221–2229 (1992)

    Google Scholar 

  13. Ollinger, N., Richard, G.: A Particular Universal Cellular Automaton. In: Proc. International Workshop on The Complexity of Simple Programs (CSP 2008), pp. 205–214 (2008)

    Google Scholar 

  14. Scharanko, A., Oliveira, P.: Derivation of one-dimensional, reversible, number-conserving cellular automata rules. In: Proc. 15th International Workshop on Cellular Automata and Discrete Complex Systems (Automata 2009), pp. 335–345 (2009)

    Google Scholar 

  15. Tanimoto, N., Imai, K.: A Characterization of von Neumann Neighbor number-conserving cellular automata. Journal of Cellular Automata 4(1), 39–54 (2009)

    MATH  MathSciNet  Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Artiom Alhazov
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • 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)

Publish with us

Policies and ethics