Learning of finite unions of tree patterns with repeated internal structured variables from queries

In the field of Web mining, a Web page can be represented by a rooted tree T such that every internal vertex of T has ordered children and string data such as tags or texts are assigned to edges of T. A term tree is an ordered tree pattern, which has ordered tree structures and variables, and is suited for a representation of a tree structured pattern in Web pages. A term tree t is allowed to have a repeated variable which occurs in t more than once. In this paper, we consider the learnability of finite unions of term trees with repeated variables in the query learning model of Angluin (1988). We present polynomial time learning algorithms for finite unions of term trees with repeated variables by using superset and restricted equivalence queries. Moreover we show that there exists no polynomial time learning algorithm for finite unions of term trees by using restricted equivalence, membership and subset queries. This result indicates the hardness of learning finite unions of term trees in the query learning model.