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@inproceedings{837103,
author = {Klíma, Ondřej and Polák, Libor},
address = {Berlin Heidelberg (Germany)},
booktitle = {Developments in Language Theory},
keywords = {varieties of languages; piecewise testable languages; syntactic monoid},
language = {eng},
location = {Berlin Heidelberg (Germany)},
isbn = {978-3-540-85779-2},
pages = {479-490},
publisher = {Springer-Verlag},
title = {Hierarchies of piecewise testable languages},
year = {2008}
}
TY - JOUR
ID - 837103
AU - Klíma, Ondřej - Polák, Libor
PY - 2008
TI - Hierarchies of piecewise testable languages
PB - Springer-Verlag
CY - Berlin Heidelberg (Germany)
SN - 9783540857792
KW - varieties of languages
KW - piecewise testable languages
KW - syntactic monoid
N2 - The classes of languages which are boolean combinations of languages of the form $A^*a_1A^*a_2A^*\dots A^*a_\ell A^*$, where $a_1,\dots, a_\ell\in A,\ell\le k$, for a fixed $k\ge 0$, form a natural hierarchy within piecewise testable languages and have been studied in papers by Simon, Blanchet-Sadri, Volkov and others. The main issues were the existence of finite bases of identities for the corresponding pseudovarieties of monoids and generating monoids for these pseudovarieties. Here we deal with similar questions concerning the finite unions and positive boolean combinations of the languages of the form above. In the first case the corresponding pseudovarieties are given by a single identity, in the second case there are finite bases for $k$ equal to 1 and 2 and there is no finite basis for $k\ge 4$ (the case $k=3$ remains open). All the pseudovarieties are generated by a single algebraic structure.
ER -
KLÍMA, Ondřej and Libor POLÁK. Hierarchies of piecewise testable languages. In \textit{Developments in Language Theory}. Berlin Heidelberg (Germany): Springer-Verlag, 2008, p.~479-490. ISBN~978-3-540-85779-2.
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