Minimum and non-minimum time solutions to the firing squad synchronization problem

Abstract

In this paper we present a survey on the minimum and non minimum time solutions to the Firing Squad Synchronization Problem. Particular emphasis is on the contribution given by Jozef Gruska, in honor of which this article is dedicated. The problem consists in synchronizing a Cellular Automata (CA) whose cells work at discrete steps at unison. The first cell is initially in a particular state, called the General, and all the others are in a Latent state. The problem is solved when, all the cells enter for the first time and simultaneously a Firing state. In its original and basic formulation, the cells are arranged as a line, here we consider also other shapes like rings, rectangular grids and toruses. Also other variations of the problem are considered, such as the limited link capacitiesand different numbers and positions of the General state. We consider both the minimum time needed to synchronize the CA and some algorithms synchronizing in particular times. Some open problems are also proposed.