Ordered Term Tree Languages which Are Polynomial Time Inductively Inferable from Positive Data

Abstract

In the fields of data mining and knowledge discovery, many semistructured data such as HTML/XML files are represented by rooted trees t such that all children of each internal vertex of t are ordered and t has edge labels. In order to represent structural features common to such semistructured data, we propose a regular term tree which is a rooted tree pattern consisting of ordered tree structures and internal structured variables. For a regular ordered term tree t, the term tree language of t, denoted by L(t), is the set of all trees which are obtained from t by substituting arbitrary trees for all variables in t.

In this paper, we consider a polynomial time learnability of the class OTTL = {L(t) ∣ t ∈ OTT} from positive data, where OTT denotes the set of all regular ordered term trees. First of all, we present a polynomial time algorithm for solving the minimal language problem for OTT which is, given a set of labeled trees S, to find a term tree t in OTT such that L(t) is minimal among all term tree languages which contain all trees in S. Moreover, by using this algorithm and the polynomial time algorithm for solving the membership problem for OTT in our previous work [15], we show that OTTL is polynomial time inductively inferable from positive data. This result is an extension of our previous results in [14].