Decision Algorithms for Cellular Automata States Based on Periodic Boundary Condition

  • Byung-Heon Kang
  • Jun-Cheol Jeon
  • Kee-Young Yoo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)


Das et al. have reported characterization of reachable/non-reachable CA states recently. Their scheme has only offered the characterization under a null boundary CA (NBCA). However, in hardware implementation, a periodic boundary CA (PBCA) is suitable for constructing cost-effective schemes such as a linear feedback shift register structure because of its circular property. Thus, this paper provides two decision algorithms for classification of reachable/non-reachable state and group/non-group CA based on periodic boundary condition.


Periodic Boundary Condition Cellular Automaton Cellular Automaton Decision Algorithm Reachable State 
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  1. 1.
    Neumann, J.V.: The Theory of Self Reproducing Automata. In: Burks, A.W. (ed.), Univ. of Illinois Press, Urbana and London (1996)Google Scholar
  2. 2.
    Wolfram, S.: Statistical Mechanics of Cellular Automata. Rev. Mod. Phys. 55, 601–644 (1983)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Martin, O., Odlyzko, A.M., Wolfram, S.: Algebraic properties of cellular automata. Commun. Math. Phys. 93, 219–258 (1984)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Pries, W., Thanailakis, A., Card, H.C.: Group properties of cellular automata and VLSI application. IEEE Trans. Comput. 12, 1013–1024 (1986)CrossRefGoogle Scholar
  5. 5.
    Chaudhuri, P.P., Choudhury, D.R., Nandi, S., Chattopadhyay, S.: Additive Cellular Automata Theory and Applications. IEEE Computer Society Press, USA (1997)MATHGoogle Scholar
  6. 6.
    Wuensche, A.: Attractor Basins of Discrete Networks. Cognitive Science Research Paper, The University of Sussex (1997)Google Scholar
  7. 7.
    Das, S., Sikdar, B.K., Chaudhuri, P.P.: Characterization of Reachable/Nonreachable Cellular Automata States. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 813–822. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Byung-Heon Kang
    • 1
  • Jun-Cheol Jeon
    • 1
  • Kee-Young Yoo
    • 1
  1. 1.Dept. of Computer EngineeringKyungpook National UniversityDaeguKorea

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