A New Time-Optimum Synchronization Algorithm for Rectangle Arrays

Authors:
Hiroshi Umeo;Hiroki Uchino
Affiliations:
(Correspd.) Faculty of Information Science and Technology, University of Osaka Electro-Communication, Neyagawa-shi, Hatsu-cho, 18-8, Osaka, 572-8530, Japan. {umeo, uchino}@umeolab.osakac.ac.jp;Faculty of Information Science and Technology, University of Osaka Electro-Communication, Neyagawa-shi, Hatsu-cho, 18-8, Osaka, 572-8530, Japan. {umeo, uchino}@umeolab.osakac.ac.jp
Venue:
Fundamenta Informaticae - Membrane Computing
Year:
2008

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Abstract

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 so far. In the present paper, we propose a new optimum-time algorithm for synchronizing two-dimensional cellular automata. The algorithm can synchronize any two-dimensional rectangle array of size m × n in optimum m + n + max(m, n) − 3 steps. A partial implementation of the algorithm for small cellular arrays is also given.