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”.
This work was partially supported by the Esprit Basic Research Action “Algebraic and Syntactical Methods In Computer Science” and by a Grant of the French Government.
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© 1995 Springer-Verlag Berlin Heidelberg
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Róka, Z. (1995). The firing squad synchronization problem on Cayley graphs. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_146
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DOI: https://doi.org/10.1007/3-540-60246-1_146
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