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
E-mail: , , ,
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