Publication Details
On Operations over Language Families
Krčmář Radim, Ing. (DIFS FIT BUT)
Kövári Adam, Mgr. (DIFS FIT BUT)
Beníčková Zuzana, Ing. (DIFS FIT BUT)
language operations, language families, closure properties, finer approach, new trend, set theory
Let O and F be an operation and a language family, respectively.
So far, in terms of closure properties, the classical language theory has only investigated whether O(F) is strictly included in F, where O(F) is the family resulting from O applied to all members of F. If O(F) is strictly included F, F is closed under O; otherwise, it is not.
This paper proposes a finer and wider approach to this investigation. Indeed, it studies almost all possible set-based relations between F and O(F), including O(F) = empty set; F is not a subset of O(F), O(F) is not a subset of F, F intersection O(F) is not empty set; F intersection O(F) = empty set, O(F) is not empty set; O(F) = F; and F is a subset of O(F).
Many operations are studied in this way.
A sketch of application perspectives and open problems closes the paper.
@ARTICLE{FITPUB11900,
author = "Alexander Meduna and Radim Kr\v{c}m\'{a}\v{r} and Adam K{\"{o}}v\'{a}ri and Zuzana Ben\'{i}\v{c}kov\'{a}",
title = "On Operations over Language Families",
pages = "255--282",
journal = "Computer Science Journal of Moldova",
volume = 27,
number = 3,
year = 2019,
ISSN = "1561-4042",
language = "english",
url = "https://www.fit.vut.cz/research/publication/11900"
}