Publication details

Subhierarchies of the Second Level in the Straubing-Thrien Hierarchy

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KLÍMA Ondřej POLÁK Libor

Year of publication 2011
Type Article in Periodical
Magazine / Source International Journal of Algebra and Computation
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Positive varieties of languages; polynomial operator
Description In a recent paper we assigned to each positive variety V and each nonnegative integer k the class of all finite unions of finite intersections or Boolean combinations of the languages of the form L0*(a1)L1*(a2)L2*...(am)Lm*, where a1,...,am are letters, L0, ...,Lm are in the variety V and k > m. For these polynomial operators on a wide class of varieties we gave a certain algebraic counterpart in terms of identities satisfied by syntactic (ordered) monoids of languages considered. Here we apply our constructions to particular examples of varieties of languages obtaining four hierarchies of (positive) varieties. Two of them have the 3/2 level of the Straubing–Thérien hierarchy as their limits, and two others tend to the level two of this hierarchy. We concentrate here on the existence of finite bases of identities for corresponding pseudovarieties of (ordered) monoids and we are looking for inclusions among those varieties.
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