Analysis of Hybrid Group Cellular Automata

  • Sung-Jin Cho
  • Un-Sook Choi
  • Yoon-Hee Hwang
  • Han-Doo Kim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)


In this paper, we analyze a Linear Hybrid Group Cellular Automata(LHGCA) C and the complemented group CA derived from C with rules 60, 102 and 204. And we give the conditions for the complement vectors which determine the state transition of the CA dividing the entire state space into smaller spaces of equal maximum cycle lengths. And we show the relationship between cycles of complemented group CA. Our results extend and generalize Mukhopadhyay’s results.


State Transition Cellular Automaton Cellular Automaton State Transition Matrix Block Matrice 
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.
    Von Neumann, J.: The theory of self-reproducing automata. In: Burks, A.W. (ed.), Univ. of Illinois Press, Urbana and London (1966)Google Scholar
  2. 2.
    Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644 (1983)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Thatcher, J.: Universality in Von Neumann cellular model, Tech. Rep. 03105-30-T, ORA, University of Michigan (1964)Google Scholar
  4. 4.
    Lee, C.: Synthesis of a cellular universal machine using 29-state model of Von Neumann. In: The University of Michigan Engineering Summer Conferences (1964)Google Scholar
  5. 5.
    Hennie, F.C.: Iterative arrays of logical circuits. Academic, New York (1961)Google Scholar
  6. 6.
    Das, A.K., Chaudhuri, P.P.: Efficient characterization of cellular automata. Proc. IEE (Part E) 137, 81–87 (1964)Google Scholar
  7. 7.
    Das, A.K., Chaudhuri, P.P.: Vector space theoretic analysis of additive cellular automata and its application for pseudo-exhaustive test pattern generation. IEEE Trans. Comput. 42, 340–352 (1993)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Nandi, S., Kar, B.K., Chaudhuri, P.P.: Theory and applications of cellular automata in cryptography. IEEE Trans. Computers 43, 1346–1357 (1994)CrossRefGoogle Scholar
  9. 9.
    Mukhopadhyay, D., Chowdhury, D.R.: Characterization of a class of complemented group cellular automata. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 775–784. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Chakraborty, S., Chowdhury, D.R., Chaudhuri, P.P.: Theory and application of nongroup cellular automata for synthesis of easily testable finite state machines. IEEE Trans. Computers 45, 769–781 (1996)MATHCrossRefGoogle Scholar
  11. 11.
    Nandi, S., Chaudhuri, P.P.: Analysis of periodic and intermediate boundary 90/150 cellular automata. IEEE Trans. Computers 45(1), 1–12 (1996)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Cho, S.J., Choi, U.S., Hwang, Y.H., Pyo, Y.S., Kim, H.D., Kim, K.S., Heo, S.H.: Computing phase shifts of maximum-length 90/150 cellular automata sequences. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 31–39. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Cho, S.J., Choi, U.S., Kim, H.D.: Analysis of complemented CA derived from a linear TPMACA. Computers and Mathematics with Applications 45, 689–698 (2003)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Cho, S.J., Choi, U.S., Kim, H.D.: Behavior of complemented CA whose complement vector is acyclic in a linear TPMACA. Mathematical and Computer Modelling 36, 979–986 (2002)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Cho, S.J., Hwang, Y.H., Choi, U.S., Kim, H.D., Pyo, Y.S.: Characterization of a class of the complemented CA derived from linear uniform CA (submitted)Google Scholar
  16. 16.
    Sen, S., Shaw, C., Chowdhury, D.R., Ganguly, N., Chaudhuri, P.P.: Cellular automata based cryptosystem. In: Deng, R.H., Qing, S., Bao, F., Zhou, J. (eds.) ICICS 2002. LNCS, vol. 2513, pp. 303–314. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Mukherjee, M., Ganguly, N., Chaudhuri, P.P.: Cellular automata based authentication. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 259–269. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Elspas, B.: The theory of autonomous linear sequential networks. TRE Trans. on Circuits CT-6(1), 45–60 (1959)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sung-Jin Cho
    • 1
  • Un-Sook Choi
    • 2
  • Yoon-Hee Hwang
    • 3
  • Han-Doo Kim
    • 4
  1. 1.Division of Mathematical SciencesPukyong National UniversityBusanKorea
  2. 2.Department of Multimedia EngineeringTongmyong UniversityBusanKorea
  3. 3.Department of Information SecurityGraduate School, Pukyong National UniversityBusanKorea
  4. 4.Institute of Mathematical Sciences and School of Computer Aided ScienceInje UniversityGimhaeKorea

Personalised recommendations