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Learning of Elementary Formal Systems with Two Clauses Using Queries
Hirotaka KATO Satoshi MATSUMOTO Tetsuhiro MIYAHARA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E92D
No.2
pp.172180 Publication Date: 2009/02/01 Online ISSN: 17451361
DOI: 10.1587/transinf.E92.D.172 Print ISSN: 09168532 Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science) Category: Keyword: computational learning theory, query learning, learning of logic programs,
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Summary:
An elementary formal system, EFS for short, is a kind of logic program over strings, and regarded as a set of rules to generate a language. For an EFS Γ, the language L(Γ) denotes the set of all strings generated by Γ. We consider a new form of EFS, called a restricted twoclause EFS, and denote by rEFS the set of all restricted twoclause EFSs. Then we study the learnability of rEFS in the exact learning model. The class rEFS contains the class of regular patterns, which is extensively studied in Learning Theory. Let Γ_{*} be a target EFS in rEFS of learning. In the exact learning model, an oracle for superset queries answers "yes" for an input EFS Γ in rEFS if L(Γ) is a superset of L(Γ_{*}), and outputs a string in L(Γ_{*})L(Γ), otherwise. An oracle for membership queries answers "yes" for an input string w if w is included in L(Γ_{*}), and answers "no", otherwise. We show that any EFS in rEFS is exactly identifiable in polynomial time using membership and superset queries. Moreover, for other types of queries, we show that there exists no polynomial time learning algorithm for rEFS by using the queries. This result indicates the hardness of learning the class rEFS in the exact learning model, in general.

