On the closedness of nilpotent DR tree languages under Boolean operations

This note deals with the closedness of nilpotent deterministic root-to-frontier tree languages with respect to the Boolean operations union, intersection and complementation. Necessary and sufficient conditions are given under which the union of two deterministic tree languages is also deterministic. The paper ends with a characterization of the largest subclass of the class of nilpotent deterministic root-to-frontier tree languages closed under the formation of complements

Rectangular algebras as tree recognizers

We consider finite rectangular algebras of finite type as tree recognizers. The type is represented by a ranked alphabet Σ. We determine the varieties of finite rectangular Σ-algebras and show that they form a Boolean lattice in which the atoms are minimal varieties of finite Σ-algebras consisting of projection algebras. We also describe the corresponding varieties of Σ-tree languages and compare them with some other varieties studied in the literature. Moreover, we establish the solidity properties of these varieties of finite algebras and tree languages. Rectangular algebras have been previously studied by R. Pöschel and M. Reichel (1993), and we make use of some of their results

On monotone languages and their characterization by regular expressions

In one of their papers, F. Gécseg and B. Imreh gave a characterization for monotone string languages by regular expressions. It has turned out that the monotone string languages are exactly those languages that can be represented by finite unions of seminormal chain languages. In this paper a similar characterization is given for monotone DR-languages