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Regular grammars with truth values in lattice-ordered monoid and their languages
Authors:Li Sheng  Yongming Li
Affiliation:(1) Institute of Fuzzy Systems, College of Mathematics and Information Science, Shaanxi Normal University, Xi"rsquo"an, 710062, China
Abstract:In this study, we introduce the concept of lattice-valued regular grammars. Such grammars have become a necessary tool for the analysis of fuzzy finite automata. The relationship between lattice-valued finite automata (LA) and lattice-valued regular grammars (LRG) are discussed and we get the following results, for a given LRG, there exists an LA such that they accept the same languages, and vice versa. We also show the equivalence between deterministic lattice-valued regular grammars and deterministic lattice-valued finite automata.
Keywords:Fuzzy finite automata  Fuzzy regular grammar  Fuzzy regular language  Lattice-ordered monoid
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