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A Synchronization Problem in Two-Dimensional Cellular Automata

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Natural Computing

Part of the book series: Proceedings in Information and Communications Technology ((PICT,volume 1))

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Abstract

The firing squad synchronization problem on cellular automata has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed so far. In the present paper, we give a survey on recent developments in firing squad synchronization algorithms for large-scale two-dimensional cellular automata. Several state-efficient implementations of the two-dimensional synchronization algorithms are 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. Beyer, W.T.: Recognition of topological invariants by iterative arrays. Ph.D. Thesis, MIT, p. 144 (1969)

    Google Scholar 

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

    Google Scholar 

  4. Goto, E.: A minimal time solution of the firing squad problem. Dittoed course notes for Applied Mathematics 298. Harvard University, pp. 52–59 (1962)

    Google Scholar 

  5. Grasselli, A.: Synchronization of cellular arrays: The firing squad problem in two dimensions. Information and Control 28, 113–124 (1975)

    Article  MATH  MathSciNet  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. 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 

  8. Moore, F.R., Langdon, G.G.: A generalized firing squad problem. Information and Control 12, 212–220 (1968)

    Article  MATH  Google Scholar 

  9. Nguyen, H.B., Hamacher, V.C.: Pattern synchronization in two-dimensional cellular space. Information and Control 26, 12–23 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  10. Romani, F.: On the fast synchronization of tree connected networks. Information Sciences 12, 229–244 (1977)

    Article  MathSciNet  Google Scholar 

  11. Schmid, H.: Synchronisationsprobleme für zelluläre Automaten mit mehreren Generälen. Diplomarbeit, Universität Karsruhe (2003)

    Google Scholar 

  12. Settle, A., Simon, J.: Smaller solutions for the firing squad. Theoretical Computer Science 276, 83–109 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Shinahr, I.: Two- and three-dimensional firing squad synchronization problems. Information and Control 24, 163–180 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  14. Szwerinski, H.: Time-optimum solution of the firing-squad-synchronization-problem for n-dimensional rectangles with the general at an arbitrary position. Theoretical Computer Science 19, 305–320 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  15. Umeo, H.: A simple design of time-efficient firing squad synchronization algorithms with fault-tolerance. IEICE Trans. on Information and Systems E87-D(3), 733–739 (2004)

    Google Scholar 

  16. Umeo, H., Hisaoka, M., Akiguchi, S.: Twelve-state optimum-time synchronization algorithm for two-dimensional rectangular cellular arrays. In: UC 2005. LNCS, vol. 3699, pp. 214–223. Springer, Heidelberg (2005)

    Google Scholar 

  17. Umeo, H., Hisaoka, M., Michisaka, K., Nishioka, K., Maeda, M.: Some new generalized synchronization algorithms and their implementations for large scale cellular automata. In: Calude, C.S., Dinneen, M.J., Peper, F. (eds.) UMC 2002, vol. 2509, pp. 276–286. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Umeo, H., Hisaoka, M., Sogabe, T.: A survey on optimum-time firing squad synchronization algorithms for one-dimensional cellular automata. Intern. J. of Unconventional Computing 1, 403–426 (2005)

    Google Scholar 

  19. Umeo, H., Hisaoka, M., Teraoka, M., Maeda, M.: Several new generalized linear- and optimum-time synchronization algorithms for two-dimensional rectangular arrays. In: Margenstern, M. (ed.) MCU 2004, vol. 3354, pp. 223–232. Springer, Heidelberg (2005)

    Google Scholar 

  20. Umeo, H., Maeda, M., Hisaoka, M., Teraoka, M.: A state-efficient mapping scheme for designing two-dimensional firing squad synchronization algorithms. Fundamenta Informaticae 74(4), 603–623 (2006)

    MATH  MathSciNet  Google Scholar 

  21. Umeo, H., Uchino, H.: A new time-optimum synchronization algorithm for two-dimensional cellular arrays. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds.) EUROCAST 2007. LNCS, vol. 4739, pp. 604–611. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Umeo, H., Yamawaki, T., Shimizu, N., Uchino, H.: Modeling and simulation of global synchronization processes for large-scale-of two-dimensional cellular arrays. In: Proc. of Intern. Conf. on Modeling and Simulation, AMS 2007, pp. 139–144 (2007)

    Google Scholar 

  23. Varshavsky, V.I., Marakhovsky, V.B., Peschansky, V.A.: Synchronization of Interacting Automata. Mathematical Systems Theory 4(3), 212–230 (1970)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Umeo, H. (2009). A Synchronization Problem in Two-Dimensional Cellular Automata. In: Suzuki, Y., Hagiya, M., Umeo, H., Adamatzky, A. (eds) Natural Computing. Proceedings in Information and Communications Technology, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-88981-6_20

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  • DOI: https://doi.org/10.1007/978-4-431-88981-6_20

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-88980-9

  • Online ISBN: 978-4-431-88981-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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