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Special Issue on Cellular Automata Theory and ApplicationsNo Access

A FAMILY OF SMALLEST SYMMETRICAL FOUR-STATE FIRING SQUAD SYNCHRONIZATION PROTOCOLS FOR RING ARRAYS

    An existence or non-existence of five-state firing squad synchronization protocol has been a longstanding and famous open problem for a long time. In this paper, we answer partially to this problem by proposing a family of smallest four-state firing squad synchronization protocols that can synchronize any one-dimensional ring cellular arrays of length n = 2k for any positive integer k. The number four is the smallest one in the class of synchronization protocols proposed so far.

    A preliminary version of this work was presented at the International Workshop on Cellular Automata: AUTOMATA 2008 (chaired by A. Adamatzky), held at Bristol in June, 2008.

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