## Abstract

We consider the class R^{2}, consisting of conjunctions of two unate DNF formulas. This class is a generalization of the class of 2-clause CNF formulas, and of the class of unate DNF formulas, both of which are properly learnable in polynomial time with membership and equivalence queries. We show that R^{2} can be properly learned with a polynomial number of polynomial-size membership and equivalence queries, but that it cannot be learned in polynomial time unless P = NP. Thus the barrier to learning R^{2} is computational rather than informational. In proving our results, we use recent techniques developed for the membership and equivalence query model, as well as Bshouty's work on the monotone dimension. We pose some related open questions on learning DNF formulas of small monotone dimension.

Original language | English (US) |
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Pages | 255-265 |

Number of pages | 11 |

State | Published - 1996 |

Event | Proceedings of the 1996 9th Annual Conference on Computational Learning Theory - Desenzano del Garda, Italy Duration: Jun 28 1996 → Jul 1 1996 |

### Other

Other | Proceedings of the 1996 9th Annual Conference on Computational Learning Theory |
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City | Desenzano del Garda, Italy |

Period | 6/28/96 → 7/1/96 |

## ASJC Scopus subject areas

- Computational Mathematics