A faster algorithm for the FSSP in one-dimensional CA with multiple speeds

03/30/2020

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by   Thomas Worsch, et al.

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In cellular automata with multiple speeds for each cell i there is a positive integer p_i such that this cell updates its state still periodically but only at times which are a multiple of p_i. Additionally there is a finite upper bound on all p_i. Manzoni and Umeo have described an algorithm for these (one-dimensional) cellular automata which solves the Firing Squad Synchronization Problem. This algorithm needs linear time (in the number of cells to be synchronized) but for many problem instances it is slower than the optimum time by some positive constant factor. In the present paper we derive lower bounds on possible synchronization times and describe an algorithm which is never slower and in some cases faster than the one by Manzoni and Umeo and which is close to a lower bound (up to a constant summand) in more cases.