Classification of CA Rules Targeting Synthesis of Reversible Cellular Automata

  • Sukanta Das
  • Biplab K. Sikdar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)


This paper reports classification of CA (cellular automata) rules targeting efficient synthesis of reversible cellular automata. An analytical framework is developed to explore the properties of CA rules for 3-neighborhood 1-dimensional CA. It is found that in two-state 3-neighborhood CA, the CA rules fall into 6 groups depending on their potential to form reversible CA. The proposed classification of CA rules enables synthesis of reversible CA in linear time.


Cellular Automaton Cellular Automaton Group Rule State Transition Diagram Unique Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cattel, K., Muzio, J.C.: Synthesis of One Dimensional Linear Hybrid Cellular Automata. IEEE Trans. on CAD 15, 325–335 (1996)Google Scholar
  2. 2.
    Pal Chaudhuri, P., Roy Chowdhury, D., Nandi, S., Chatterjee, S.: Additive Cellular Automata – Theory and Applications, vol. 1. IEEE Computer Society Press, California (1997)MATHGoogle Scholar
  3. 3.
    Das, S.: Theory and A pplications of Nonlinear C ellular Automata I n VLSI Design. PhD thesis, Bengal Engineering And Science University, Shibpur (2006)Google Scholar
  4. 4.
    Das, S., Kundu, A., Sikdar, B.K., Chaudhuri, P.P.: Design of Nonlinear CA Based TPG Without Prohibited Pattern Set In Linear Time. Journal of Electronic Testing: Theory and Applications 21, 95–109 (2005)CrossRefGoogle Scholar
  5. 5.
    Das, S., Sikdar, B.K., Chaudhuri, P.: Characterization of Reachable/Nonreachable Cellular Automata States. In: Proceedings of Sixth International Conference on Cellular Automata for Research and Industry, ACRI 2004, The Netherlands, October 2004, pp. 813–822 (2004)Google Scholar
  6. 6.
    Margara, L., Mauri, G., Cattaneo, G., Formenti, E.: On the dynamical behavior of chaotic cellular automata. Theoretical Computer Science 217, 31–51 (1999)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Toffoli, T., Margolus, N.H.: Invertible cellular automata: A review. Physica D 45, 229–253 (1990)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55(3), 601–644 (1983)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sukanta Das
    • 1
  • Biplab K. Sikdar
    • 2
  1. 1.Dept. of Information TechnologyBengal Engineering & Sc. UniversityShibpur, HowrahIndia
  2. 2.Dept. of Computer Sc. & TechnologyBengal Engineering & Sc. UniversityShibpur, HowrahIndia

Personalised recommendations