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A Design of Symmetrical Six-State 3n-Step Firing Squad Synchronization Algorithms and Their Implementations

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Cellular Automata (ACRI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4173))

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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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Authors and Affiliations

  1. Univ. of Osaka Electro-Communication, Neyagawa-shi, Hastu-cho, 18-8, Osaka, 572-8530, Japan

    Hiroshi Umeo, Masashi Maeda & Kazuaki Hongyo

Authors
  1. Hiroshi Umeo
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  2. Masashi Maeda
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  3. Kazuaki Hongyo
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Editors and Affiliations

  1. Laboratory of Mathematics, Physics and Systems, University of Perpignan, 52, Paul Alduy Avenue, 66860, Perpignan, Cedex, France

    Samira El Yacoubi

  2. Computer Science Department, University of Geneva, Switzerland

    Bastien Chopard

  3. Research Center on Complex Systems and Artificial Intelligence (CSAI) Department of Computer Science, Systems and Communication (DISCo), University of Milan, Bicocca viale Sarca, 336, 20126, Milan, (Italy)

    Stefania Bandini

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© 2006 Springer-Verlag Berlin Heidelberg

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40929-8

  • Online ISBN: 978-3-540-40932-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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