A Construction of Number-Conserving Firing Squad Synchronization Algorithm on One-Dimensional Arrays

We propose a number-conserving firing squad synchronization algorithm, which is nearly a time-optimum solution to the firing squad synchronization problem (FSSP). The algorithm can be implemented on a number-conserving cellular automaton. In the number-conserving cellular automata (NC-CA), any state of cells is represented by a single non-negative integer and total summed number of states in any configuration is conserved throughout its operations. The NC-CA can be thought as a model of the physical conservation law of mass or energy. Our synchronization algorithm has multiple firing states and can synchronize any array of length n in 2n-1 steps.