文章基本信息

标题：On Local Symmetries and Universality in Cellular Automata
本地全文：下载
作者：Laurent Boyer ; Guillaume Theyssier
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2009
卷号：3
页码：195-206
DOI：10.4230/LIPIcs.STACS.2009.1836
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. In this paper, we show that the asymptotic density of universal cellular automata is 1 in several families of CA defined by local symmetries. We extend results reviously established for captive cellular automata in two significant ways. First, our results apply to well-known families of CA (e.g. the family of outer-totalistic CA containing the Game of Life) and, second, we obtain such density results with both increasing number of states and increasing neighbourhood. Moreover, thanks to universality-preserving encodings, we show that the universality problem remains undecidable in some of those families.
关键词：Cellular automata; Universality; Asymptotic density