### Abstract

Valiant introduced a computational model of learning by examples, and gave a precise definition of learnability based on the model. Since then, much effort has been devoted to characterize learnable classes of concepts on this model. Among such learnable classes is the one, denoted k-term MDNF, consisting of monotone disjunctive normal form formulae with at most k terms. In literature, k-term MDNF is shown to be learnable under the assumption that examples are drawn according to the uniform distribution. In this paper we generalize the result to obtain the statement that k-term MDNF is learnable even if positive examples are drawn according to such distribution that the maximum of the ratio of the probabilities of two positive examples is bounded from above by some polynomial.

Original language | English |
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Title of host publication | Algorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings |

Editors | Shuji Doshita, Koichi Furukawa, Klaus P. Jantke, Toyaki Nishida |

Publisher | Springer Verlag |

Pages | 197-207 |

Number of pages | 11 |

ISBN (Print) | 9783540573692 |

DOIs | |

Publication status | Published - 1993 |

Event | 3rd Workshop on Algorithmic Learning Theory, ALT 1992 - Tokyo, Japan Duration: 1992 Oct 20 → 1992 Oct 22 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 743 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Workshop on Algorithmic Learning Theory, ALT 1992 |
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Country | Japan |

City | Tokyo |

Period | 92/10/20 → 92/10/22 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings*(pp. 197-207). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 743 LNAI). Springer Verlag. https://doi.org/10.1007/3-540-57369-0_39