Learning of Finite Unions of Tree Patterns with Repeated Internal Structured Variables from Queries

The exact learning model by Angluin (1988) is a mathematical model of learning via queries in computational learning theory. A term tree is a tree pattern consisting of ordered tree structures and repeated structured variables, which occur more than once. Thus, a term tree is suited for representing common tree structures based on tree-structured data, such as HTML and XML files on the Web. In this paper, we consider the learnability of finite unions of term trees with repeated variables in the exact learning model. 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 exact learning model.