A Transition Rule Set for the First 2-D Optimum-Time Synchronization Algorithm

  • Hiroshi Umeo
  • Kaori Ishida
  • Koutarou Tachibana
  • Naoki Kamikawa
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 2)


The firing squad synchronization problem on cellular automata has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed for two-dimensional cellular arrays. In the present paper, we reconstruct a real-coded transition rule set for an optimum-time synchronization algorithm proposed by Shinahr [11], known as the first optimum-time synchronization algorithm for two-dimensional rectangle arrays. Based on our computer simulation, it is shown that the proposed rule set consists of 28-state, 12849 transition rules and has a validity for the synchronization for any rectangle arrays of size m ×n such that 2 ≤ m, n ≤ 500.


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Copyright information

© Springer Tokyo 2010

Authors and Affiliations

  • Hiroshi Umeo
    • 1
  • Kaori Ishida
    • 1
  • Koutarou Tachibana
    • 1
  • Naoki Kamikawa
    • 1
  1. 1.Univ. of Osaka Electro-CommunicationOsakaJapan

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