### 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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Title of host publication | Proceedings of the Annual ACM Conference on Computational Learning Theory |

Editors | Anon |

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 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Mathematics

### Cite this

*Proceedings of the Annual ACM Conference on Computational Learning Theory*(pp. 255-265)

**Learning conjunctions of two unate DNF formulas : Computational and informational results.** / Feigelson, Aaron; Hellerstein, Lisa.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Proceedings of the Annual ACM Conference on Computational Learning Theory.*pp. 255-265, Proceedings of the 1996 9th Annual Conference on Computational Learning Theory, Desenzano del Garda, Italy, 6/28/96.

}

TY - CHAP

T1 - Learning conjunctions of two unate DNF formulas

T2 - Computational and informational results

AU - Feigelson, Aaron

AU - Hellerstein, Lisa

PY - 1996

Y1 - 1996

N2 - We consider the class R2, 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 R2 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 R2 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.

AB - We consider the class R2, 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 R2 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 R2 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.

UR - http://www.scopus.com/inward/record.url?scp=0030382734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030382734&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0030382734

SP - 255

EP - 265

BT - Proceedings of the Annual ACM Conference on Computational Learning Theory

A2 - Anon, null

ER -