How to synchronize square arrays in optimum-time — A new square synchronization algorithm

The firing squad synchronization problem (FSSP,for short) on cellular automata has been studied extensively for more than fifty years, and a rich variety of synchronization algorithms have been proposed for one- and two-dimensional cellular automata. In the present paper, we propose a new optimum-time FSSP algorithm for two-dimensional square cellular automata. The algorithm can synchronize any square arrays of size n × n with a general at one corner at exactly In - 2 steps. It is based on a new technique called one-sided recursive halving marking and is quite different from the well known classical FSSP algorithm proposed by Beyer [1969] and Shinahr [1974].