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Title:
automata theory based on complete residuated lattice-valued logic: turing machines
Author: Wu Lihua ; Qiu Daowen ; Xing Hongyan
Source: Fuzzy Sets and Systems
Issued Date: 2012
Volume: 208, Pages:43-66
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
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.
Language: 英语
WOS ID: WOS:000309803300003
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/14732
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Wu Lihua,Qiu Daowen,Xing Hongyan. automata theory based on complete residuated lattice-valued logic: turing machines[J]. Fuzzy Sets and Systems,2012-01-01,208:43-66.
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