A 4-state solution to the Firing Squad Synchronization Problem based on hybrid rule 60 and 102 cellular automata

Abstract: In this paper, we present a 4-state solution to the Firing Squad Synchronization Problem (FSSP) based on hybrid rule 60/102 Cellular Automata(CA). This solution solves the problem on the line of length 2^n with two generals. Previous work on FSSP for 4-state systems focused mostly on linear cellular automata, where synchronizes an infinite number of lines but not all possible lines. We give time-optimal solutions to synchronize an infinite number of lines by rule 60 and rule 102 respectively, and construct a hybrid rule 60 and 102 states transition table. Compared to the known solutions of cellular automata, the hybrid CA way is simpler and faster, the minimal time is (n-1) step.