Two-Dimensional Cellular Automata Synchronizers

We study a firing squad synchronization problem that gives a finite-state protocol for synchronizing large-scale cellular automata. In this paper, we give a survey on recent developments in designing optimumand non-optimum-time synchronization algorithms and present their state-efficient implementations for two-dimensional cellular arrays. Several simple, state-efficient mapping schemes are proposed for embedding one-dimensional firing squad synchronization algorithms onto two-dimensional arrays. Throughout this paper we focus our attention to the algorithms for synchronizing two-dimensional rectangular arrays with the general at one corner of the array.