On Reversible Cellular Automata with Finite Cell Array

  • Shuichi Inokuchi
  • Kazumasa Honda
  • Hyen Yeal Lee
  • Tatsuro Sato
  • Yoshihiro Mizoguchi
  • Yasuo Kawahara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3699)

Abstract

Discrete quantum cellular automata are cellular automata with reversible transition. This paper deals with 1d cellular automata with finite cell array and triplet local transition rules. We present the necessary condition of local transition rules for cellular automata to be reversible, and prove the reversibility of some cellular automata.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dow, R.A.: Additive Cellular Automata and Global Injectivity. Physica D 110, 67–91 (1997)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Goles, E., Martinez, S.: Neural and automata networks - dynamical behavior and applications. Kluwer Academic Publishers, Dordrecht (1990)MATHGoogle Scholar
  3. 3.
    Inokuchi, S., et al.: Computational analysis of cellular automata with triplet transition rule. Research Reports on Information Science and Electrical Engineering of Kyushu University 1(1), 79–84 (1996) (in Japanese)Google Scholar
  4. 4.
    Inokuchi, S., Mizoguchi, Y.: Generalized Partitioned Quantum Cellular Automata and Quantization of Classical CA. Int. Journ. of Unconventional Computing 1, 149–160 (2005)Google Scholar
  5. 5.
    Kobuchi, Y., Nishio, H.: Some regular state sets in the system of one-dimensional iterative automata. Information Sciences 5, 199–216 (1973)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Lee, H.-Y., Kawahara, Y.: Transition diagrams of finite cellular automata. Bull. Inform. Cybernet. 28, 47–69 (1996)MATHMathSciNetGoogle Scholar
  7. 7.
    Morita, K., Harao, M.: Computation universality of one-dimensional reversible (injective) cellular automata. Transactions of the IEICE E 72, 758–762 (1989)Google Scholar
  8. 8.
    Watrous, J.: On one-dimensional quantum cellular automata. In: Proceedings on the 36th Annual Symposium on Foundations of Computer Science, pp. 528–537 (1995)Google Scholar
  9. 9.
    Wolfram, S.: Random sequence generation by cellular automata. Advances in Applied Mathematics 7, 123–169 (1986)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Wolfram, S.: A New Kind of Science, pp. 435–457, 1017–1021. Wolfram Media, Inc., Illinois (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Shuichi Inokuchi
    • 1
  • Kazumasa Honda
    • 2
  • Hyen Yeal Lee
    • 3
  • Tatsuro Sato
    • 4
  • Yoshihiro Mizoguchi
    • 1
  • Yasuo Kawahara
    • 2
  1. 1.Faculty of MathematicsKyushu University 33FukuokaJapan
  2. 2.Department of InformaticsKyushu University 33FukuokaJapan
  3. 3.School of Computer EngineeringPusan National UniversityPusanKorea
  4. 4.Oita National College of TechnologyOitaJapan

Personalised recommendations