一维多速度CA中FSSP的快速算法
A faster algorithm for the FSSP in one-dimensional CA with multiple speeds
摘要：
在每个单元$i$具有多个速度的元胞自动机中，存在正整数$p_i$，使得该单元仍然周期性地更新其状态，但仅在$p_i$的倍数的时间更新。此外，所有$p_i$都有一个有限的上界。Manzoni和Umeo描述了这些（一维）细胞自动机的算法，解决了射击队同步问题。该算法需要线性时间（在要同步的单元数量中），但对于许多问题实例，它比最佳时间慢一些正的常数因子。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，它永远不会慢，在某些情况下比曼佐尼和Umeo的一个更快，这是接近一个下限（一个常数和）在更多的情况下。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
