This paper investigates the interaction of mind changes and anomalies for inductive inference of recursive real-valued functions. We show that the criteria for inductive inference of recursive real-valued functions by bounding the number of mind changes and anomalies preserve the same hierarchy as that of recursive functions, if the length of each anomaly as an interval is bounded. However, we also show that, without bounding it, the hierarchy of some criteria collapses. More precisely, while the class of recursive real-valued functions inferable in the limit allowing no more than one anomaly is properly contained in the class allowing just two anomalies, the latter class coincides with the class allowing arbitrary and bounded number of anomalies.

In this paper, we consider a data mining problem for semi-structured data. Modeling semi-structured data as labeled ordered trees, we present an efficient algorithm for discovering frequent substructures from a large collection of semi-structured data. By extending the enumeration technique developed by Bayardo (SIGMOD'98) for discovering long itemsets, our algorithm scales almost linearly in the total size of maximal tree patterns contained in an input collection depending mildly on the size of the longest pattern. We also developed several pruning techniques that significantly speed-up the search. Experiments on Web data show that our algorithm runs efficiently on real-life datasets combined with proposed pruning techniques in the wide range of parameters.

The elementary formal system (EFS, for short) is a kind of logic program which directly manipulates character strings. This paper outlines in brief the authors' studies on algorithmic learning theory developed in the framework of EFS's. We define two important classes of EFS's and a new hierarchy of various language classes. Then we discuss EFS's as logic programs. We show that EFS's form a good framework for inductive inference of languages by presenting model inference system for EFS's in Shapiro's sense. Using the framework we also show that inductive inference from positive data and PAC-learning are both much more powerful than they have been believed. We illustrate an application of our theoretical results to Molecular Biology.