SUBHIERARCHIES OF THE SECOND LEVEL IN THE STRAUBING–THÉRIEN HIERARCHY

ONDŘEJ KLÍMA, LIBOR POLÁK
2011 International journal of algebra and computation  
In a recent paper we assigned to each positive variety V and a fixed natural number k the class of all (positive) boolean combinations of the restricted polynomials, i.e. the languages of the form L0a1L1a2 . . . a L , where ≤ k, a1, . . . , a are letters and L0, . . . , L are from the variety V. For this polynomial operator on a wide class of varieties we gave a certain algebraic counterpart which works with identities satisfied by syntactic (ordered) monoids of considered languages. Here we
more » ... ly our constructions for particular examples of varieties of languages obtaining four hierarchies of (positive) varieties which have the 3/2 level and the second level of the Straubing-Thérien hierarchy as their limits. We concentrate here on inclusions among such varieties and we also discuss the existence of finite bases of identities for corresponding pseudovarieties of (ordered) monoids.
doi:10.1142/s021819671100690x fatcat:hhu4fq4lzjeqholbzp7ziezuc4