关于 Fuzzyω正则语言的一个注记

通过引入ω-Nerode等价关系,fuzzy前逆缀ω-语言,闭左逆语言等概念来研究语言的化数性质,得到了(1)fuzzyω正则语言可由一些具有有限指标集的等价类来表示;(2)fuzzy前逆缀ω-语言是fuzzyω正则语言iff由L定义的ω-Nerode等价关系的指标集是有限的.

Note on Fuzzy ω-Regular Languages

In this paper the notion of the ω-Nerode equivalence relation over ∑* is introduced, and the concepts of fuzzy prefix-inverse-related ω-language over ∑ and left-inverse-closed languge. On this base,the following results are obtained:fuzzy prefix-inverse-related ω-language over ∑ is fuzzyω-regular language if and only if the index of the ω-Nerode equivalence relati defined by L is finite,fuzzy ω-regular language over ∑ is represented by the union of some equivalence classes of some equivalence relation with finite index, left-invariant over ∑ω. Thus in a class of ω-language with prefix-inverse-related ω-language or left-inverse-closed ω-language, the characteristics of fuzzyω-regular language is given from algebra and set viewpoints. This is a foundation for deep researches on fuzzy finite-state automaton and fuzzy regular language.