Skip to main content
SpringerLink
Log in

Complexity of limit language of the elementary cellular automaton of rule 22

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

In this paper, the limit set of the elementary cellular automaton of rule 22 is considered. The limit language is defined from limit set and its complexity is studied by using formal language theory. It is proved that this language is not a regular language. This result shows that the dynamics of this cellular automaton is actually complicated.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wang Yi, Jiang Zhisong. Evolution complexity of the elementary cellular automaton of rule 22, Appl Math J Chinese Univ Ser B, 2002, 17(4):404–412.

    MATH  Google Scholar 

  2. Lam L. Introduction to Nonlinear Physics, New York: Springer-Verlag, 1997.

    MATH  Google Scholar 

  3. Wolfram S. Theory and Application of Cellular Automata, Singapore: World Scientic, 1986.

    Google Scholar 

  4. Wolfram S. Twenty problems in the theory of cellular automata, Physica Script, 1985, T9:170–183.

    Article  Google Scholar 

  5. Wolfram S. Computation theory of cellular automata, Comm Math Phys, 1984, 96:15–57.

    Article  MATH  Google Scholar 

  6. Hurd L P. Recursive cellular automata invariant sets, Complex Systems, 1990, 4:119–129.

    MATH  Google Scholar 

  7. Hurd L P. Nonrecursive cellular automata invariant sets, Complex Systems, 1990, 4:131–138.

    MATH  Google Scholar 

  8. Jiang Zhisong. A complexity analysis of the elementary cellular automaton of rule 122 (in Chinese), Chinese Science Bulletin, 2000, 45(18):2007–2012.

    Google Scholar 

  9. Xie Huimin. The complexity of limit languages of cellular automata: an example, J Systems Science and Complexity, 2001, 14:17–30

    MATH  Google Scholar 

  10. Hopcroft J E, Ullman J D, Introduction ot Automata Theory Languages and Computation, Boston: Addison-Wesley, 1979.

    Google Scholar 

  11. Rosenberg G, Saloman A. Handbook of Formal Languages, New York: Springer-Verlag, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Math., East China Univ., of Science and Technology, 200237, Shanghai, China

    Jiang Zhisong & Wang Yi

  2. Dept. of Math., Suzhou Univ., 215006, Suzhou, China

    Jiang Zhisong & Wang Yi

  3. Faculty of Engineering, Hiroshima Univ., 739-8527, Higashi Hiroshima, Japan

    Jiang Zhisong & Wang Yi

Authors
  1. Jiang Zhisong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported partly by the National Natural Science Foundation of China (10101016) and Tian Yuan Foundation of China (10126020).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhisong, J., Yi, W. Complexity of limit language of the elementary cellular automaton of rule 22. Appl. Math. Chin. Univ. 20, 268–276 (2005). https://doi.org/10.1007/s11766-005-0002-z

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-005-0002-z

MR Subject Classification

Keywords

Search

Navigation