A smallest five-state solution to the firing squad synchronization problem

Authors:
Hiroshi Umeo;Takashi Yanagihara
Affiliations:
Univ. of Osaka Electro-Communication, Osaka, Japan;Univ. of Osaka Electro-Communication, Osaka, Japan
Venue:
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Year:
2007

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Abstract

An existence or non-existence of five-state firing squad synchronization protocol has been a long-standing, famous open problem for a long time. In this paper, we answer partially to this problem by proposing a smallest five-state firing squad synchronization algorithm that can synchronize any one-dimensional cellular array of length n = 2k in 3n-3 steps for any positive integer k. The number five is the smallest one known at present in the class of synchronization protocols proposed so far.