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A Comparative Study of Optimum-Time Synchronization Algorithms for One-Dimensional Cellular Automata – A Survey –

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3305))

Abstract

We present a survey and a comparison of the quantitative and qualitative aspects of the optimum-time synchronization algorithms developed thus far for one-dimensional cellular arrays. Several new results and viewpoints are also given.

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References

  1. Balzer, R.: An 8-state minimal time solution to the firing squad synchronization problem. Information and Control 10, 22–42 (1967)

    Article  Google Scholar 

  2. Hans-D, Gerken: Über Synchronisations - Probleme bei Zellularautomaten. Diplomarbeit, Institut für Theoretische Informatik, Technische Universität Braunschweig, p. 50 (1987)

    Google Scholar 

  3. Goto, E.: A minimal time solution of the firing squad problem. Dittoed course notes for Applied Mathematics, vol. 298, pp. 52–59. Harvard University, Cambridge (1962); With an illustration in color

    Google Scholar 

  4. Goto, E.: Some puzzles on automata. In: Kitagawa, T. (ed.) Toward computer sciences, Kyouritsu, pp. 67–91 (1966) (in Japanease)

    Google Scholar 

  5. Mazoyer, J.: An overview of the firing squad synchronization problem. LNCS, vol. 316, pp. 82–93. Springer, Heidelberg (1986)

    Google Scholar 

  6. Mazoyer, J.: A six-state minimal time solution to the firing squad synchronization problem. Theoretical Computer Science 50, 183–238 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  7. Mazoyer, J.: On optimal solutions to the firing squad synchronization problem. Theoretical Computer Science 168, 367–404 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mazoyer, J.: A minimal-time solution to the FSSP without recursive call to itself and with bounded slope of signals. Draft version, p. 8 (1997)

    Google Scholar 

  9. Minsky, M.: Computation: Finite and infinite machines, pp. 28–29. Prentice-Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  10. Moore, E.F.: The firing squad synchronization problem. In: Moore, E.F. (ed.) Sequential Machines, Selected Papers, pp. 213–214. Addison-Wesley, Reading (1964)

    Google Scholar 

  11. Nishimura, J., Sogabe, T., Umeo, H.: A design of optimum-time firing squad synchronization algorithm on 1-bit cellular automaton. In: Proc. of the 8th International Symposium on Artificial Life and Robotics, vol. 2, pp. 381–386 (2003)

    Google Scholar 

  12. Umeo, H.: A note on firing squad synchronization algorithms-A reconstruction of Goto’s first-in-the-world optimum-time firing squad synchronization algorithm. In: Kutrib, M., Worsch, T. (eds.) Proc. of Cellular Automata Workshop, p. 65 (1996)

    Google Scholar 

  13. Umeo, H., Kamikawa, N.: 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, 257–275 (2002)

    MATH  MathSciNet  Google Scholar 

  14. Umeo, H., Nishimura, J., Sogabe, T.: 1-bit inter-cell communication cellular algorithms (invited lecture). In: Proc. of the Tenth Intern. Colloquium on Differentia Equations, held in Plovdiv in 1999, International Journal of Differential Equations and Applications, vol. 1A(4), pp. 433–446 (2000)

    Google Scholar 

  15. Umeo, H., Sogabe, T., Nomura, Y.: Correction, optimization and verification of transition rule set for Waksman’s firing squad synchronization algorithm. In: Proc. of the Fourth Intern. Conference on Cellular Automata for Research and Industry, pp. 152–160. Springer, Heidelberg (2000)

    Google Scholar 

  16. Vollmar, R.: On Cellular Automata with a Finite Number of State Change. Computing, Supplementum 3, 181–191 (1981)

    Google Scholar 

  17. Vollmar, R.: Some remarks about the “Efficiency” of polyautomata. International Journal of Theoretical Physics 21(12), 1007–1015 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  18. Waksman, A.: An optimum solution to the firing squad synchronization problem. Information and Control 9, 66–78 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  19. Yunes, J.B.: Seven-state solution to the firing squad synchronization problem. Theoretical Computer Science 127, 313–332 (1994)

    Article  MATH  MathSciNet  Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Umeo, H., Hisaoka, M., Sogabe, T. (2004). A Comparative Study of Optimum-Time Synchronization Algorithms for One-Dimensional Cellular Automata – A Survey –. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_6

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  • DOI: https://doi.org/10.1007/978-3-540-30479-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23596-5

  • Online ISBN: 978-3-540-30479-1

  • eBook Packages: Springer Book Archive

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