Advertisement

Experimental Finitization of Infinite Field-Based Generalized FSSP Solution

  • Luidnel Maignan
  • Jean-Baptiste Yunès
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8751)

Abstract

In a previous work (see [3]) we presented a general scheme to solve the 1D Generalized Firing Squad Synchronization Problem. We designed it in a modular way using the concept of fields (open CA). The solution was not designed as a finite cellular automaton because we needed unbounded integers as states for distance fields, and the recursive nature of the algorithm leaded to a unbounded number of fields. In this paper, we show as claimed, that this approach does lead to a finite cellular automaton. We exhibit a transformation function from infinite to finite states and write a program that generates the associated finite transition table while checking its validity and the conservation of the input-output behavior of the original cellular automaton.

Keywords

cellular automata automata minimization quotient automata firing squad synchronization problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balzer, R.: An 8-state minimal time solution to the firing squad synchronization problem. Information and Control 10, 22–42 (1967)CrossRefGoogle Scholar
  2. 2.
    Maignan, L., Gruau, F.: Integer gradient for cellular automata: Principle and examples. In: Self-Adaptive and Self-Organizing Systems Workshops, SASOW 2008, pp. 321–325 (2008)Google Scholar
  3. 3.
    Maignan, L., Yunès, J.-B.: A spatio-temporal algorithmic point of view on firing squad synchronisation problem. In: Sirakoulis, G.C., Bandini, S. (eds.) ACRI 2012. LNCS, vol. 7495, pp. 101–110. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Maignan, L., Yunès, J.B.: Moore and von Neumann neighborhood n-dimensional generalized firing squad solutions using fields. In: AFCA 2013 Workshop. CANDAR 2013 Conference, Matsuyama, Japan, December 4-6 (2013)Google Scholar
  5. 5.
    Mazoyer, J.: A six-state minimal time solution to the firing squad synchronization problem. Theoretical Computer Science 50, 183–238 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Moore, E.E.: Sequential Machines, Selected Papers, pp. 213–214. Addison-Wesley (1964)Google Scholar
  7. 7.
    Noguchi, K.: Simple 8-state minimal time solution to the firing squad synchronization problem. Theoretical Computer Science 314(3), 303–334 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Schmidt, H., Worsch, T.: The firing squad synchronization problem with many generals for one-dimensional CA. In: Levy, J.-J., Mayr, E.W., Mitchell, J.C. (eds.) 3rd IFIP International Conference on Theoretical Computer Science. IFIP, vol. 155, pp. 111–124. Springer, Boston (2004)Google Scholar
  9. 9.
    Yunès, J.B.: An intrinsically non minimal-time Minsky-like 6-states solution to the firing squad synchronization problem. RAIRO-Theor. Inf. Appl. 42, 55–68 (2008)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Luidnel Maignan
    • 1
  • Jean-Baptiste Yunès
    • 2
  1. 1.LACLUniversié Paris-Est CréteilCréteilFrance
  2. 2.LIAFAUniversité Paris-DiderotParisFrance

Personalised recommendations