Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Introduction to the concept of recursiveness of fuzzy functions
Fuzzy Sets and Systems
Fuzzy subsets: a constructive approach
Fuzzy Sets and Systems
Fuzzifying topology based on complete residuated lattice-valued logic (I)
Fuzzy Sets and Systems
SIAM Journal on Computing
Computable analysis: an introduction
Computable analysis: an introduction
Fuzzy logic: mathematical tools for approximate reasoning
Fuzzy logic: mathematical tools for approximate reasoning
On a class of fuzzy computable functions
Fuzzy Sets and Systems
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Automata theory based on quantum logic: some characterizations
Information and Computation
Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
A probabilistic model of computing with words
Journal of Computer and System Sciences
Artificial Intelligence
Automata theory based on quantum logic: Reversibilities and pushdown automata
Theoretical Computer Science
On the computing power of fuzzy Turing machines
Fuzzy Sets and Systems
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Multi-valued Logics, Effectiveness and Domains
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Lattice-valued fuzzy Turing machines: Computing power, universality and efficiency
Fuzzy Sets and Systems
Interactive Computation: Stepping Stone in the Pathway From Classical to Developmental Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Turing machines, transition systems, and interaction
Information and Computation
Fuzzy and probabilistic programs
Information Sciences: an International Journal
Supervisory control of fuzzy discrete event systems: a formal approach
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
A formal model of computing with words
IEEE Transactions on Fuzzy Systems
Computing with words via Turing machines: a formal approach
IEEE Transactions on Fuzzy Systems
Fuzzy Turing Machines: Variants and Universality
IEEE Transactions on Fuzzy Systems
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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.