Automata theory based on unsharp quantum logic

doi:10.1017/S0960129509007701

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	Automata theory based on unsharp quantum logic
	Shang, Yun 1; Lu, Xian 1; Lu, Ruqian 1,2
	2009-08-01
发表期刊	MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
ISSN	0960-1295
卷号	19 期号:4 页码:737-756
摘要	By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and only if a certain kind of distributive law holds for the sum operation. We introduce the notions of (quantum) finite automata based on these two unsharp quantum structures, and discuss closure properties of languages and the subset construction of automata. We show that the universal validity of some important properties (such as sum, concatenation and subset constructions) depend heavily on the above distributive law. These generalise results about automata theory based on sharp quantum logic.
DOI	10.1017/S0960129509007701
语种	英语
资助项目	NSFC Major Research Program[60496324] ; NSFC Major Research Program[60736011] ; NSFC Major Research Program[60603002] ; 863project[2007AA01Z325] ; 973project[2009CB320701]
WOS研究方向	Computer Science
WOS类目	Computer Science, Theory & Methods
WOS记录号	WOS:000269103100003
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9128
专题	中国科学院数学与系统科学研究院
通讯作者	Shang, Yun
作者单位	1.Acad Sinica, AMSS, Math Inst, Beijing 100190, Peoples R China 2.Fudan Univ, Shanghai Key Lab Intelligent Informat Proc, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	Shang, Yun,Lu, Xian,Lu, Ruqian. Automata theory based on unsharp quantum logic[J]. MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE,2009,19(4):737-756.
APA	Shang, Yun,Lu, Xian,&Lu, Ruqian.(2009).Automata theory based on unsharp quantum logic.MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE,19(4),737-756.
MLA	Shang, Yun,et al."Automata theory based on unsharp quantum logic".MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE 19.4(2009):737-756.