Experimental Finitization of Infinite Field-Based Generalized FSSP Solution
In a previous work (see ) 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.
Keywordscellular automata automata minimization quotient automata firing squad synchronization problem
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- 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
- 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
- 6.Moore, E.E.: Sequential Machines, Selected Papers, pp. 213–214. Addison-Wesley (1964)Google Scholar
- 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