文章基本信息

标题：On Operations over Language Families
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作者：Alexander Meduna ; Radim Krčmář ; Adam Kövári 等
期刊名称：Computer Science Journal of Moldova
印刷版ISSN：1561-4042
出版年度：2019
卷号：27
期号：3
页码：255-282
出版社：Institute of Mathematics and Computer Science
摘要：Let O and F be an operation and a language family, respec-tively. So far, in terms of closure properties, the classical lan-guage theory has only investigated whether O(F) ⊆ F, whereO(F) is the family resulting from O applied to all members of F.If O(F) ⊆ F, F is closed under O; otherwise, it is not.This paper proposes a finer and wider approach to this inves-tigation. Indeed, it studies almost all possible set-based relationsbetween F and O(F), including O(F) = ∅; F 6⊂ O(F), O(F) 6⊂ F,F∩O(F) 6= ∅; F∩O(F) = ∅, O(F) 6= ∅; O(F) = F; and F ⊂ O(F).Many operations are studied in this way. A sketch of applicationperspectives and open problems closes the paper.
关键词：language operations; language families; closure properties; finer approach; new trend; set theory.