Definite tree languages.

TL;DR: It is proved that every family of regular tree languages which can be characterized by syntactic monoids is such a variety, but that the converse does not hold.

TL;DR: This paper presents an inference algorithm for learning a k-testable tree language that runs in polynomial time with respect to the size of the sample used and studies the tree language classes in relation to other well known ones.

TL;DR: This work provides structural descriptions of certain varieties of finite tree automata closed under a version of the cascade product, called the Moore product, and obtain decidable characterizations of the expressive power of certain fragments of CTL on finite trees.

TL;DR: A modal operator is associated with each language belonging to a given class of regular tree languages and the cascade product of tree automata is used to give an algebraic characterization of the expressive power of the resulting logic.