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An Efficient Mapping Scheme for Embedding Any One-Dimensional Firing Squad Synchronization Algorithm onto Two-Dimensional Arrays

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Cellular Automata (ACRI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2493))

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Abstract

An efficient mapping scheme is proposed for embedding any one-dimensional firing squad synchronization algorithm onto 2-D arrays, and some new 2-D synchronization algorithms based on the mapping scheme are presented. The proposed mapping scheme can be readily applied to the design of synchronization algorithms with fault tolerance, algorithms operating on multi-dimensional cellular arrays, and for the generalized case where the general is located at an arbitrary position on the array. A six-state algorithm is developed that can synchronize any m × n rectangular array in 2(m + n) - 4 steps. In addition, we develop a nine-state optimum-time synchronization algorithm on square arrays. We progressively reduce the number of internal states of each cellular automaton on square and rectangular arrays, achieving nine states for a square array and six states for a rectangular array. These are the smallest number of states reported to date for synchronizing rectangular and square arrays.

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Authors and Affiliations

  1. Osaka Electro-Communication University, Neyagawa-shi, Hatsu-cho 18-8, Osaka, 572-8530, Japan

    Masashi Maeda & Norio Fujiwara

Authors
  1. 1Hiroshi Umeo
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  2. Masashi Maeda
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  3. Norio Fujiwara
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Systems and Communication, University of Milano-Bicocca, Via Bicocca degli Arcimboldi, 8, 20126, Milan, Italy

    Stefania Bandini

  2. Computer Science Department, University of Geneva, 24, Rue du General Dufour, 1211, Geneva 4, Switzerland

    Bastien Chopard

  3. Computer Science Institute Faculty of Sciences, University of Lausanne, 1015, Lausanne, Switzerland

    Marco Tomassini

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© 2002 Springer-Verlag Berlin Heidelberg

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Umeo, 1., Maeda, M., Fujiwara, N. (2002). An Efficient Mapping Scheme for Embedding Any One-Dimensional Firing Squad Synchronization Algorithm onto Two-Dimensional Arrays. In: Bandini, S., Chopard, B., Tomassini, M. (eds) Cellular Automata. ACRI 2002. Lecture Notes in Computer Science, vol 2493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45830-1_7

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  • DOI: https://doi.org/10.1007/3-540-45830-1_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44304-9

  • Online ISBN: 978-3-540-45830-2

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