A Small Five-State Non-Optimum-Time Solution to the Firing Squad Synchronization Problem: A Geometrical Approach

Authors:
Hiroshi Umeo;Takashi Yanagihara
Affiliations:
(Correspd.) Faculty of Information Science and Technology, University of Osaka Electro-Communication, Neyagawa-shi, Hatsu-cho, 18-8, Osaka, 572-8530, Japan. {umeo, yanagihara}@cyt.osakac.ac.jp;Faculty of Information Science and Technology, University of Osaka Electro-Communication, Neyagawa-shi, Hatsu-cho, 18-8, Osaka, 572-8530, Japan. {umeo, yanagihara}@cyt.osakac.ac.jp
Venue:
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Year:
2009

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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 small five-state firing squad synchronization algorithm that can synchronize any one-dimensional cellular array of length n = 2$^k$ in 3n − 3 steps for any positive integer k.