Efficient learning of context-free grammars from positive structural examples

Authors:
Yasubumi Sakakibara
Affiliations:
International Institute for Advanced Study of Social Information Science (IIAS-SIS), Fujitsu Limited, 140, Miyamoto, Numazu, Shizuoka, 410-03 Japan
Venue:
Information and Computation
Year:
1992

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Abstract

In this paper, we introduce a new normal form for context-free grammars, called reversible context-free grammars, for the problem of learning context-free grammars from positive-only examples. A context-free grammar G = (N, @S, P, S) is said to be reversible if (1) A - @a and B - @a in P implies A = B and (2) A - @aB@b and A - @aC@b in P implies B = C. We show that the class of reversible context-free grammars can be identified in the limit from positive samples of structural descriptions and there exists an efficient algorithm to identify them from positive samples of structural descriptions, where a structural description of a context-free grammar is an unlabelled derivation tree of the grammar. This implies that if positive structural examples of a reversible context-free grammar for the target language are available to the learning algorithm, the full class of context-free languages can be learned efficiently from positive samples.