Equations and monoid varieties of dot-depth one and two
Theoretical Computer Science
A proof of Simon's theorem on piecewise testable languages
Theoretical Computer Science
Handbook of formal languages, vol. 1
Automata, Languages, and Machines
Automata, Languages, and Machines
Varieties Of Formal Languages
On Logical Descriptions of Regular Languages
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Polynomial Operators on Classes of Regular Languages
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
On Schützenberger products of semirings
DLT'10 Proceedings of the 14th international conference on Developments in language theory
On the learnability of shuffle ideals
The Journal of Machine Learning Research
| Hi-index | 0.00 |
The classes of languages which are boolean combinations of languages of the form $$A^*a_1A^*a_2A^*\dots A^*a_\ell A^*, \text{ where } a_1,\dots ,a_\ell\in A,\ \ell\le k\,,$$for a fixed k茂戮驴 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 kequal to 1 and 2 and there is no finite basis for k茂戮驴 4 (the case k= 3 remains open). All the pseudovarieties are generated by a single algebraic structure.