State-Efficient Firing Squad Synchronization Protocols for Communication-Restricted Cellular Automata

  • Hiroshi Umeo
  • Takashi Yanagihara
  • Masaru Kanazawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)


In this paper, we study a trade-off between internal states and communication bits in firing squad synchronization protocols for k-bit communication-restricted cellular automata (CA k − bit ) and propose several time-optimum state-efficient bit-transfer-based synchronization protocols. It is shown that there exists a 1-state CA5 − bit that can synchronize any n cells in 2n-2 optimum-step. The result is interesting, since we know that there exists no 4-state synchronization algorithm on conventional O(1)-bit communication cellular automata. A bit-transfer complexity is also introduced to measure the efficiency of synchronization protocols. We show that Ω (n logn) bit-transfer is a lower-bound for synchronizing n cells in (2n-2) steps. In addition, each optimum-time/non-optimum-time synchronization protocols, presented in this paper, has an O(n 2) bit-transfer complexity, respectively.


Internal State Cellular Automaton Cellular Automaton Quiescent State State Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hiroshi Umeo
    • 1
  • Takashi Yanagihara
    • 1
  • Masaru Kanazawa
    • 1
  1. 1.Univ. of Osaka Electro-CommunicationOsakaJapan

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