## Abstract

In this paper we study the query complexity of finding local minimum points of a boolean function. This task occurs frequently in exact learning algorithms for many natural classes, such as monotone DNF, O(log n)-term DNF, unate DNF and decision trees. On the negative side, we prove that any (possibly randomized) algorithm that produces a local minimum of a function f chosen from a sufficiently 'rich' concept class, using a membership oracle for f, must ask Ω(n^{2}) membership queries in the worst case. In particular, this lower bound applies to the class of decision trees. A simple algorithm is known that achieves this lower bound. On the positive side, we show that for the class O(log n)-term DNF finding local minimum points requires only Θ(n log n) membership queries (and more generally Θ(nt) membership queries for t-term DNF with t ≤ n). This efficient procedure improves the time and query complexity of known learning algorithms for the class O(log n)-term DNF.

Original language | English GB |
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Title of host publication | Proceedings of the 1998 11th Annual Conference on Computational Learning Theory, Madison, WI, USA, |

Pages | 294-302 |

Number of pages | 9 |

DOIs | |

State | Published - 1 Jan 1998 |

Externally published | Yes |

Event | Proceedings of the 1998 11th Annual Conference on Computational Learning Theory - Madison, WI, USA Duration: 24 Jul 1998 → 26 Jul 1998 |

### Conference

Conference | Proceedings of the 1998 11th Annual Conference on Computational Learning Theory |
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City | Madison, WI, USA |

Period | 24/07/98 → 26/07/98 |

## ASJC Scopus subject areas

- Computational Mathematics