On optimal solutions to the firing squad synchronization problem

The one-dimensional firing squad synchronization problem (FSSP) is considered. The problem is to construct a generic automaton of a one dimensional cellular network made of a segment of n identical machines such that, if at the starting time (t identical with 1) all finite automata of the cellular network are in a quiescent state L and no meaningful information is exchanged, the segment evolves in such a way that at the firing time t(n) all automata enter simultaneously and for the very first time into the firing state F. It is observed that if the notion of optimality in time is well defined for a solution to the FSSP, the notion of size is more complex.