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@article{1840697, author = {Klíma, Ondřej and Kostolányi, Peter}, article_number = {October}, doi = {http://dx.doi.org/10.1016/j.ic.2021.104709}, keywords = {Geometrical closure; Commutative closure; Variety of languages; Star-free language}, language = {eng}, issn = {0890-5401}, journal = {Information and Computation}, title = {Geometrically closed positive varieties of languages}, url = {https://www.sciencedirect.com/science/article/pii/S0890540121000249#!}, volume = {288}, year = {2022} }
TY - JOUR ID - 1840697 AU - Klíma, Ondřej - Kostolányi, Peter PY - 2022 TI - Geometrically closed positive varieties of languages JF - Information and Computation VL - 288 IS - October SP - 1-17 EP - 1-17 PB - Elsevier SN - 08905401 KW - Geometrical closure KW - Commutative closure KW - Variety of languages KW - Star-free language UR - https://www.sciencedirect.com/science/article/pii/S0890540121000249#! N2 - A recently introduced operation of geometrical closure on formal languages is investigated from the viewpoint of algebraic language theory. Positive varieties V containing exclusively languages with regular geometrical closure are fully characterised by inclusion of V in W, a known positive variety arising in the study of the commutative closure. It is proved that the geometrical closure of a language from the intersection of W with the variety of all star-free languages SF always falls into RLT, which is introduced as a subvariety of R, the variety of languages recognised by R-trivial monoids. All classes between RLT and W∩SF are thus geometrically closed: for instance, the level 3/2 of the Straubing-Thérien hierarchy, the DA-recognisable languages, or the variety R. It is also shown that W∩SF is the largest geometrically closed positive variety of star-free languages, while there is no largest geometrically closed positive variety of regular languages. ER -
KLÍMA, Ondřej and Peter KOSTOLÁNYI. Geometrically closed positive varieties of languages. \textit{Information and Computation}. Elsevier, 2022, vol.~288, October, p.~1-17. ISSN~0890-5401. Available from: https://dx.doi.org/10.1016/j.ic.2021.104709.
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