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IMI/Publicaţii/CSJM/Ediţii/CSJM v.27, n.3 (81), 2019/

On Operations over Language Families

Authors: Alexander Meduna, Radim Krčmář, Adam Kövári, Zuzana Beníčková
Keywords: language operations; language families; closure properties; finer approach; new trend; set theory.

Abstract

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, where O(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 relations between 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 application perspectives and open problems closes the paper.

Faculty of Information Technology, Brno University of Technology
Brno, Czech Republic
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