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DOI:
:2003.14(1):9-15

量子自动机的刻画
邱道文
(中山大学,计算机科学系,广东,广州,510275;清华大学,计算机科学与技术系,北京,100084;清华大学,智能技术与系统国家重点实验室,北京,100084)
Characterizations of Quantum Automata
QIU Dao-Wen
()
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Received:July 24, 2001    Revised:October 16, 2001
> 中文摘要: 澄清了各类量子自动机之间的相互关系,并给出了量子自动机的各种等价刻画定理.引入G-量子自动机、g-量子自动机、(广义)量子自动机及G-量子文法和g-量子文法,并阐明了它们与其他量子自动机之间的等价关系.在一定条件下讨论了G(g)-量子自动机与G(g)-量子文法的等价性,从而解决了关于量子文法产生量子正规语言的问题.讨论了量子语言与正规语言的关系,特别是回答了Gudder提出的两个公开问题.最后,给出了一种减少状态空间维数的方法.
中文关键词: Hilbert空间  量子计算  自动机  文法  正规语言
Abstract:The relationships among various quantum automata are clarified, and in particular, variously equivalent characterizations of quantum automata are established. The G-quantum automata, g-quantum automata, (generalized) quantum automata, G-quantum grammars and g-quantum grammars are presented, and their connections to some of the other existing quantum automata are expounded. Under a certain condition, the equivalence between the G(g)-quantum automata and G(g)-quantum grammars is discussed. Therefore the problem of quantum grammars generating quantum regular languages is solved. The relation between quantum and regular languages is dealt with, and particularly, two open problems proposed by Gudder are answered. Finally, the method of decreasing the dimensions of spaces of states on quantum automata is given.
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基金项目:(Supported by the National Grand Fundamental Research 973 Program of China under Grant No.G1998030509 (国家重点基础研究发展规划(973)); the National Natural Science Foundation of China for Distinguished Young Scholars under Grant No.69725004 (国家杰出青年科学基金); the Natural Science Foundation of Guangdong Province of China under Grant No.020146 (广东省自然科学基金); the Young Foundation of Zhongshan University of China under Grant No.35100-1131127 (中山大学青年基金) (Supported by the National Grand Fundamental Research 973 Program of China under Grant No.G1998030509 (国家重点基础研究发展规划(973)); the National Natural Science Foundation of China for Distinguished Young Scholars under Grant No.69725004 (国家杰出青年科学基金); the Natural Science Foundation of Guangdong Province of China under Grant No.020146 (广东省自然科学基金); the Young Foundation of Zhongshan University of China under Grant No.35100-1131127 (中山大学青年基金)
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邱道文.量子自动机的刻画.软件学报,2003,14(1):9-15

QIU Dao-Wen.Characterizations of Quantum Automata.Journal of Software,2003,14(1):9-15