Abstract
We assign to each positive variety $\mathcal V$ and each natural number k the class of all (positive) Boolean combinations of the restricted polynomials, i.e. the languages of the form $L_0a_1 L_1a_2\dots a_\ell L_\ell, \text{ where } \ell\leq k$ , a 1,...,a ℓ are letters and L 0,...,L ℓ are languages from the variety $\mathcal V$ . For this polynomial operator we give a certain algebraic counterpart which works with identities satisfied by syntactic (ordered) monoids of languages considered. We also characterize the property that a variety of languages is generated by a finite number of languages. We apply our constructions to particular examples of varieties of languages which are crucial for a certain famous open problem concerning concatenation hierarchies. 2000 Classification: 68Q45 Formal languages and automata.
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