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| automata theory based on complete residuated lattice-valued logic: turing machines | |
| Wu Lihua; Qiu Daowen; Xing Hongyan | |
| 2012 | |
| Source | Fuzzy Sets and Systems
 |
| ISSN | 1650114 |
| Volume | 208Pages:43-66 |
| English Abstract | Automata theory based on complete residuated lattice-valued logic, called L-valued finite automata (L-VFAs), has been established by the second author in 2001. In view of the importance of Turing machines, in this paper, we establish a theory of Turing machines based on complete residuated lattice-valued logic, which is a continuation of L-VFAs. First, we give the definition of L-valued nondeterministic Turing machines (L-NTMs), and observe that the multitape L-NTMs have the same language-recognizing power as the single-tape L-NTMs. We give some related properties of L-valued Turing machines, and discuss computing with fuzzy letters via L-valued Turing machines. Second, we introduce the concepts of L-valued recursively enumerable languages and L-valued recursive languages, and obtain some equivalent relations. Some results concerning the characterization of n-recursively enumerable sets are given, and the super-computing power of L-valued Turing machines is investigated. We also prove that L-valued deterministic Turing machines and L-NTMs are not equivalent in the sense of recognizing or deciding languages. Finally, we show that there is no universal L-valued Turing machine. However, a universal L-valued Turing machine exists if the membership degrees of L-valued sets are restricted to a finite complete residuated lattice with universal bounds 0 and 1. © 2012 Elsevier B.V. |
| Indexed Type | ei |
| Department | (1) Department of Computer Science, Sun Yat-sen University, Guangzhou 510006, China; (2) SQIG - Instituto de Telecomunicações, Departamento de Matemática, Universidade Técnica de Lisboa, Avenida Rovisco Pais 1049-001, Lisbon, Portugal; (3) State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China; (4) College of Informatics, South China Agricultural University, Guangzhou 510642, China |
| Language | 英语 |
| WOS ID | WOS:000309803300003 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/14732 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Wu Lihua,Qiu Daowen,Xing Hongyan. automata theory based on complete residuated lattice-valued logic: turing machines[J]. Fuzzy Sets and Systems,2012,208:43-66. |
| APA | Wu Lihua,Qiu Daowen,&Xing Hongyan.(2012).automata theory based on complete residuated lattice-valued logic: turing machines.Fuzzy Sets and Systems,208,43-66. |
| MLA | Wu Lihua,et al."automata theory based on complete residuated lattice-valued logic: turing machines".Fuzzy Sets and Systems 208(2012):43-66. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| 1-s2.0-S016501141200（334KB） | 开放获取 | License | Application Full Text | |||
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