### 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, Σ, P, S) is said to be reversible if (1) A → α and B → α in P implies A = B and (2) A → αBβ and A → αCβ 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.

Original language | English |
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Pages (from-to) | 23-60 |

Number of pages | 38 |

Journal | Information and Computation |

Volume | 97 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1992 Mar |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics