An Infinite Prime Sequence Can Be Generated in Real-Time by a 1-Bit Inter-cell Communication Cellular Automaton

  • Hiroshi Umeo
  • Naoki Kamikawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2450)


It is shown that an infinite prime sequence can be generated in real-time by a cellular automaton having 1-bit inter-cell communications.


Cellular Automaton Cellular Automaton Transition Rule Unit Speed Cellular Automaton Model 
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  1. 1.
    M. Arisawa: On the generation of integer series by the one-dimensional iterative arrays of finite state machines (in Japanese). The Trans. of IECE, 71/8 Vol.54-C, No.8, pp.759–766, (1971).Google Scholar
  2. 2.
    C. R. Dyer: One-Way Bounded Cellular Automata. Information and Control, Vol.44, pp.261–281, (1980).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    P. C. Fischer: Generation of primes by a one-dimensional real-time iterative array. J. of ACM, Vol.12, No.3, pp.388–394, (1965).MATHCrossRefGoogle Scholar
  4. 4.
    I. Korec: Real-time generation of primes by a one-dimensional cellular automaton with 11 states. Proc. of 22nd Intern. Symp. on MFCS’ 97, Lecture Notes in Computer Science, 1295, pp.358–367, (1997).Google Scholar
  5. 5.
    J. Mazoyer: A minimal time solution to the firing squad synchronization problem with only one bit of information exchanged. Technical report of Ecole Normale Superieure de Lyon, No.89-03, pp.51, April, (1989).Google Scholar
  6. 6.
    J. Mazoyer: On optimal solutions to the firing squad synchronization problem. Theoret. Comput. Sci., 168, pp.367–404, (1996).MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J. Mazoyer and V. Terrier: Signals in one-dimensional cellular automata. Theoretical Computer Science, 217, pp.53–80, (1999).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A. R. Smith: Real-time language recognition by one-dimensional cellular automata. J. of Computer and System Sciences, 6, pp.233–253, (1972).MATHGoogle Scholar
  9. 9.
    V. Terrier: On real-time one-way cellular array. Theoretical Computer Science, 141, pp.331–335, (1995).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    V. Terrier: Language not recognizable in real time by one-way cellular automata. Theoretical Computer Science, 156, pp.281–287, (1996).MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    H. Umeo: Cellular Algorithms with 1-Bit Inter-Cell Communications. Proc. of MFCS’98 Satellite Workshop on Cellular Automata (Eds. T. Worsch and R. Vollmar), pp.93–104, Interner Bericht 19/98, University of Karlsruhe, (1998).Google Scholar
  12. 12.
    H. Umeo and M. Inada: A Design of Cellular Algorithms for 1-Bit Inter-Cell Communications. Proc. of the Fifth International Workshop on Parallel Image Analysis, IWPIA’97, pp.51–62, (1997).Google Scholar
  13. 13.
    H. Umeo: Linear-time recognition of connectivity of binary images on 1-bit inter-cell communication cellular automaton. Parallel Computing, 27, pp.587–599, (2001).MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    H. Umeo and N. Kamikawa: A design of real-time non-regular sequence generation algorithms and their implementations on cellular automata with 1-bit inter-cell communications. Fundamenta Informaticae, 52, No.1–3, pp.255–273, (2002).MathSciNetGoogle Scholar
  15. 15.
    T. Worsch: Linear Time Language Recognition on Cellular Automata with Restricted Communication, Proc. of LATIN 2000:Theoretical Informatics (Eds. G. H. Gonnet, D. Panario and A. Viola), LNCS 1776, pp.417–426, (2000).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hiroshi Umeo
    • 1
  • Naoki Kamikawa
    • 2
  1. 1.Osaka Electro-Communication Univ.OsakaJapan
  2. 2.Noritsu Koki Co. Ltd.UmeharaJapan

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