English

A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata

Formal Languages and Automata Theory 2012-08-15 v1 Discrete Mathematics Data Structures and Algorithms Cellular Automata and Lattice Gases

Abstract

The firing squad synchronization problem (FSSP) on cellular automata has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed for not only one-dimensional arrays but two-dimensional arrays. In the present paper, we propose a simple recursive-halving based optimum-time synchronization algorithm that can synchronize any rectangle arrays of size m*n with a general at one corner in m+n+max(m, n)-3 steps. The algorithm is a natural expansion of the well-known FSSP algorithm proposed by Balzer [1967], Gerken [1987], and Waksman [1966] and it can be easily expanded to three-dimensional arrays, even to multi-dimensional arrays with a general at any position of the array.

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Cite

@article{arxiv.1208.2761,
  title  = {A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata},
  author = {Hiroshi Umeo and Kinuo Nishide and Keisuke Kubo},
  journal= {arXiv preprint arXiv:1208.2761},
  year   = {2012}
}

Comments

In Proceedings AUTOMATA&JAC 2012, arXiv:1208.2498

R2 v1 2026-06-21T21:50:13.388Z