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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 a Libor POLÁK. Hierarchies of piecewise testable languages. In \textit{Developments in Language Theory}. Berlin Heidelberg (Germany): Springer-Verlag. s.~479-490. ISBN~978-3-540-85779-2. 2008.
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