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Criteria for Inductive Inference with Mind Changes and Anomalies of Recursive Real-Valued Functions
Eiju HIROWATARI Kouichi HIRATA Tetsuhiro MIYAHARA Setsuo ARIKAWA
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2003/02/01
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Selected Papers from LA Symposium)
Category: Computational Learning Theory
learning theory, inductive inference, real-valued function,
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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.