文章基本信息
- 标题：On the Parity Problem in One-Dimensional Cellular Automata
- 本地全文：下载
- 作者：Heater Betel ; Pedro P. B. de Oliveira ; Paola Flocchini 等
- 期刊名称：Electronic Proceedings in Theoretical Computer Science
- 电子版ISSN：2075-2180
- 出版年度：2012
- 卷号：90
- 页码：110-126
- DOI：10.4204/EPTCS.90.9
- 出版社：Open Publishing Association
- 摘要：We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to see that the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1). We then consider only odd lattices.
We are interested in determining the minimal neighbourhood that allows the problem to be solvable for any initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that there exists no radius 2 rule that can possibly solve the parity problem from arbitrary initial configurations. On the other hand, we design a radius 4 rule that converges correctly for any initial configuration and we formally prove its correctness. Whether or not there exists a radius 3 rule that solves the parity problem remains an open problem.
