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

Satoshi MATSUMOTO  Takayoshi SHOUDAI  Tomoyuki UCHIDA  Tetsuhiro MIYAHARA  Yusuke SUZUKI  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E91-D   No.2   pp.222-230
Publication Date: 2008/02/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e91-d.2.222
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science)
Category: Algorithmic Learning Theory
Keyword: 
exact learning,  computational learning theory,  finite union of tree pattern languages,  

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Summary: 
A linear term tree is defined as an edge-labeled rooted tree pattern with ordered children and internal structured variables whose labels are mutually distinct. A variable can be replaced with arbitrary edge-labeled rooted ordered trees. We consider the polynomial time learnability of finite unions of linear term trees in the exact learning model formalized by Angluin. The language L(t) of a linear term tree t is the set of all trees obtained from t by substituting arbitrary edge-labeled rooted ordered trees for all variables in t. Moreover, for a finite set S of linear term trees, we define L(S)=∪tS L(t). A target of learning, denoted by T*, is a finite set of linear term trees, where the number of edge labels is infinite. In this paper, for any set T* of m linear term trees (m ≥ 0), we present a query learning algorithm which exactly identifies T* in polynomial time using at most 2mn2 Restricted Subset queries and at most m+1 Equivalence queries, where n is the maximum size of counterexamples. Finally, we note that finite sets of linear term trees are not learnable in polynomial time using Restricted Equivalence, Membership and Subset queries.