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The firing squad synchronization problem on Cayley graphs

  • Zsuzsanna Róka
Contributed Papers Distributed Computation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)

Abstract

The Firing Squad Synchronization Problem (FSSP for short) has been intensively studied in the one-dimensional space. The problem consists in the synchronization of a segment of automata. We generalize this problem on Cayley graphs. We give minimal time solutions for (a) synchronizing all cells in all minimal paths between any pair of cells of a Cayley graph; (b) synchronizing all cells in all minimal paths starting at a given cell G (the “general”) and leading to all cells at a given distance from G in a Cayley graph. In solutions for (b), in some cases, all cells of a ball in a Cayley graph will be synchronized, in other cases this is not possible because of the existence of “culs-de-sac”.

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References

  1. 1.
    R. Balzer. A 8 state minimal time solution to the Firing Squad Synchronization Problem. Information and Control, 10:22–42, 1967.Google Scholar
  2. 2.
    C. Culik. Variation of the Firing Squad Synchronization Problem. Information Processing Letter, pages 152–157, 1989.Google Scholar
  3. 3.
    A. Machí and F. Mignosi. Garden of Eden configurations for cellular automata on Cayley graphs of groups. SIAM Journal on Discrete Mathematics, 6(1):44–56, 1993.Google Scholar
  4. 4.
    J. Mazoyer. A six states minimal time solution to the Firing Squad Synchronization Problem. Theoretical Computer Science, 50:183–238, 1987.Google Scholar
  5. 5.
    F.R. Moore and G.G. Langdon. A generalized firing squad problem. Information and Control, (12):212–220, 1968.Google Scholar
  6. 6.
    D.E. Müller and P.E. Schupp. Pushdown automata, ends, second-order logic and reachability problems. In 13th Annual ACM Symp. on the Theory of Computing, Milwaukee, 1981.Google Scholar
  7. 7.
    A. Holliger P. Rosenstiehl, J.R. Fiksel. Graph Theory and Computing, chapter Intelligent graphs: Networks of finite automata capable of solving graph problems. Lectures in Computer Science. R. C. Read, academic press edition, 1972.Google Scholar
  8. 8.
    Zs. Róka. Cellular automata on Cayley graphs. PhD thesis, Ecole Normale Supérieure de Lyon, France, July 1994.Google Scholar
  9. 9.
    Zs. Róka. The Firing Squad Synchronization Problem on Cayley graphs, preprint, 1995.Google Scholar
  10. 10.
    H. Szwerinsky. Time optimal solution for the Firing Squad Synchronization Problem for n-dimensional rectangles with the general at any position. Theoretical Computer Science, 19:305–320, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Zsuzsanna Róka
    • 1
  1. 1.Laboratoire de l'Informatique du ParallélismeEcole Normale Supérieure de LyonLyon Cedex 07France

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