Automata theory based on complete residuated lattice-valued logic: Reduction and minimization

Automata theory based on complete residuated lattice-valued logic, called L- valued finite automata ( L- VFAs), has been established by Qiu recently. In this paper, we define a kind of Mealy type of L- VFAs ( MLFAs), a generalization of L- VFAs. Two kinds of statewise equivalence relations are intro...

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Bibliographic Details
Published in:Fuzzy sets and systems 2010-06, Vol.161 (12), p.1635-1656
Main Authors: Wu, Lihua, Qiu, Daowen
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Automata theory
Circuit properties
Combinatorics. Ordered structures
Computer science
control theory
systems
Digital circuits
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Finite automata
Fuzzy regular languages
Fuzzy set theory
Information, signal and communications theory
Logic
Mathematical analysis
Mathematical methods
Mathematics
Minimization
Miscellaneous
Non-classical logic
Optimization
Order, lattices, ordered algebraic structures
Reduction
Reduction and minimization
Residuated lattices
Sciences and techniques of general use
Telecommunications and information theory
Theoretical computing
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Summary:Automata theory based on complete residuated lattice-valued logic, called L- valued finite automata ( L- VFAs), has been established by Qiu recently. In this paper, we define a kind of Mealy type of L- VFAs ( MLFAs), a generalization of L- VFAs. Two kinds of statewise equivalence relations are introduced, and a minimal form is defined. We study the existence of the minimal form of an MLFA. Then, we show that any two states can be distinguished by some word with finite length. Also, a minimization algorithm of the MLFAs is presented. In addition, we obtain a minimization algorithm for L- VFAs as well. Finally, we define L- valued languages ( L- VLs) and L- valued regular languages ( L- VRLs) recognized by L- VFAs, and provide some properties of L- VRLs.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2009.12.011