Generalized Reversibility of Topological Dynamical Systems and Cellular Automata

CSpace

	Generalized Reversibility of Topological Dynamical Systems and Cellular Automata
	Zhang, Kuize 1,2; Zhang, Lijun 1,3
	2015
发表期刊	JOURNAL OF CELLULAR AUTOMATA
ISSN	1557-5969
卷号	10 期号:5-6 页码:425-434
摘要	In this paper, we characterize the reversibility of topological dynamical systems over the limit sets. We define a new concept of generalized inverse systems for topological dynamical systems, and prove that (i) a topological dynamical system has a generalized inverse system if and only if it is injective over its limit set and its limit set is reached in finite time, and (ii) if a topological dynamical system has a generalized inverse system, these two systems have the same topological entropy. For cellular automata (CAs), a particular class of topological dynamical systems, we prove some additional properties: (iii) A CA has a generalized inverse CA if and only if it is injective over its limit set. (iv) It is undecidable whether a given CA has a generalized inverse CA.
关键词	Topological dynamical system cellular automaton generalized reversibility limit set topological entropy undecidability Drazin inverse
语种	英语
资助项目	Fundamental Research Funds for Central Universities[HEUCFX41501] ; Key Laboratory of Systems and Control, Chinese Academy of Sciences ; Program for New Century Excellent Talents in University of Ministry of Education of China ; Basic Research Foundation of Northwestern Polytechnical University[JC201230] ; National Natural Science Foundation of China[61174047]
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000364606800005
出版者	OLD CITY PUBLISHING INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21161
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Kuize
作者单位	1.Harbin Engn Univ, Coll Automat, Harbin 150001, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Beijing 100190, Peoples R China 3.Northwestern Polytech Univ, Sch Marine Sci Technol, Xian 710072, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Kuize,Zhang, Lijun. Generalized Reversibility of Topological Dynamical Systems and Cellular Automata[J]. JOURNAL OF CELLULAR AUTOMATA,2015,10(5-6):425-434.
APA	Zhang, Kuize,&Zhang, Lijun.(2015).Generalized Reversibility of Topological Dynamical Systems and Cellular Automata.JOURNAL OF CELLULAR AUTOMATA,10(5-6),425-434.
MLA	Zhang, Kuize,et al."Generalized Reversibility of Topological Dynamical Systems and Cellular Automata".JOURNAL OF CELLULAR AUTOMATA 10.5-6(2015):425-434.