Abstract
In 1994, Yunès [19] began to explore 3n-step firing squad synchronization algorithms and developed two seven-state synchronization algorithms for one-dimensional cellular arrays. His algorithms were so interesting in that he progressively decreased the number of internal states of each cellular automaton.In this paper, we propose a new symmetrical six-state 3n-step firing squad synchronization algorithm. Our result improves the seven-state 3n-step synchronization algorithms developed by Yunès [19]. The number six is the smallest one known at present in the class of 3n–step synchronization algorithms. A non-trivial and new symmetrical six-state 3n-step generalized firing squad synchronization algorithm is also given. In addition, we study a state-change complexity in 3n-step firing squad synchronization algorithms. We show that our algorithms have O(n 2) state-change complexity, on the other hand, the thread-like 3n-step algorithms developed so far have O(n logn) state-change complexity.
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Umeo, H., Maeda, M., Hongyo, K. (2006). A Design of Symmetrical Six-State 3n-Step Firing Squad Synchronization Algorithms and Their Implementations. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_21
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DOI: https://doi.org/10.1007/11861201_21
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