A design of symmetrical six-state 3n-step firing squad synchronization algorithms and their implementations

  • Authors:

  • Hiroshi Umeo;Masashi Maeda;Kazuaki Hongyo

  • Affiliations:

  • Univ of Osaka Electro-Communication, Osaka, Japan;Univ of Osaka Electro-Communication, Osaka, Japan;Univ of Osaka Electro-Communication, Osaka, Japan

  • Venue:
  • ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
  • Year:
  • 2006

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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(n2) state-change complexity, on the other hand, the thread-like 3n-step algorithms developed so far have O(n logn) state-change complexity.