A new optimum-time firing squad synchronization algorithm for two-dimensional rectangle arrays: One-sided recursive halving based

Abstract

The firing squad synchronization problem on cellular automata has been studied extensively for more than fifty years, and a rich variety of synchronization algorithms have been proposed for not only one-dimensional arrays but two-dimensional arrays. In the present paper, we propose a new optimum-time synchronization algorithm that can synchronize any two-dimensional rectangle arrays of size m × n with a general at one corner in m + n + max (m, n) - 3 steps. The algorithm is based on a simple recursive halving marking schema which helps synchronization operations on two-dimensional arrays. A proposed computer-assisted implementation of the algorithm gives a description of a two-dimensional cellular automaton in terms of a finite 384-state set and a local 112690-rule set. © 2011 Springer-Verlag.