| Notes on automata theory based on quantum logic |
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| 引用本文： | QIU DaoWen Department of Computer Science,Zhongshan University,Guangzhou 510275,China. Notes on automata theory based on quantum logic[J]. 中国科学F辑(英文版), 2007, 50(2): 154-169. DOI: 10.1007/s11432-007-0020-y |
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| 作者姓名： | QIU DaoWen Department of Computer Science Zhongshan University Guangzhou 510275 China |
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| 作者单位： | QIU DaoWen Department of Computer Science，Zhongshan University，Guangzhou 510275，China |
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| 基金项目： | 国家自然科学基金;广东省自然科学基金 |
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| 摘 要： | The main results are as follows: (1) it deals with a number of basic operations (concatenation, Kleene closure, homomorphism, complement); (2) due to a condition imposed on the implication operator for discussing some basic issues in orthomodular lattice-valued automata, this condition is investigated in detail, and it is discovered that all the relatively reasonable five implication operators in quantum logic do not satisfy this condition, and that one of the five implications satisfies such a condition iff the truth-value lattice is indeed a Boolean algebra; (3) it deals further with orthomodular lattice-valued successor and source operators; (4) an example is provided, implying that some negative results obtained in the literature may still hold in some typical orthomodular lattice-valued automata.
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| 收稿时间： | 2006-04-13 |
| 修稿时间： | 2007-01-17 |
Notes on automata theory based on quantum logic |
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| Qiu DaoWen. Notes on automata theory based on quantum logic[J]. Science in China(Information Sciences), 2007, 50(2): 154-169. DOI: 10.1007/s11432-007-0020-y |
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| Authors: | Qiu DaoWen |
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| Affiliation: | Department of Computer Science, Zhongshan University, Guangzhou 510275, China |
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| Abstract: | The main results are as follows: (1) it deals with a number of basic operations (concatenation, Kleene closure, homomorphism, complement); (2) due to a condition imposed on the implication operator for discussing some basic issues in orthomodular lattice-valued automata, this condition is investigated in detail, and it is discovered that all the relatively reasonable five implication operators in quantum logic do not satisfy this condition, and that one of the five implications satisfies such a condition iff the truth-value lattice is indeed a Boolean algebra; (3) it deals further with orthomodular lattice-valued successor and source operators; (4) an example is provided, implying that some negative results obtained in the literature may still hold in some typical orthomodular lattice-valued automata. |
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| Keywords: | quantum computing quantum logic orthomodular lattices automata |
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