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.

中文翻译：

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具有多种速度的一维 CA 中更快的 FSSP 算法

在每个单元格具有多种速度的元胞自动机中，$i$ 有一个正整数 $p_i$，这样该单元格仍然定期更新其状态，但仅在 $p_i$ 的倍数的时间。此外，所有 $p_i$ 都有一个有限的上限。Manzoni 和 Umeo 描述了这些（一维）元胞自动机的算法，该算法解决了射击小队同步问题。该算法需要线性时间（在要同步的单元格数量中），但对于许多问题实例，它比最佳时间慢一些正常数因子。在本文中，我们推导出可能的同步时间的下限，并描述了一种算法，该算法从不慢，在某些情况下比 Manzoni 和 Umeo 的算法快，并且在更多情况下接近下限（达到恒定的加数） .