On the closedness of nilpotent DR tree languages under Boolean operations

Abstract

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.