Fuzzy ω正则语言的注记

Note on Fuzzy ω-Regular Languages

定义Σω上的ω-Nerode等价关系的符号,并且定义了Σ上Fuzzy前缀逆相关ω-语言和左逆封闭语言,在这些定义的基础上,得到了Σ上Fuzzy前缀逆相关ω-语言是Fuzzyω正则语言的充分必要条件是由L定义的ω-Nerode等价关系的指数有限,Σ上Fuzzyω正则语言可以表示成Σω上一些具有有限指数的左不变等价关系的某些等价类的并集。因而在由前缀逆相关ω-语言或左逆封闭ω语言组成的ω-语言类中,Fuzzyω正则语言的代数特征就可从代数和集合论的观点给出。这为进一步研究Fuzzy有限状态自动机和Fuzzy正则语言奠定了基础。

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