## Abstract

We consider the problem of determining whether a given function f: {0, 1}^{n} → {0, 1} belongs to a certain class of Boolean functions F or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ϵ, we wou ld like to decide whether f∈F or whether it differs from every g ∈F on more than an ϵ -fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.

Original language | American English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |

Subtitle of host publication | Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings |

Editors | Luca Trevisan, Klaus Jansen, Michel Goemans, Jose D. P. Rolim |

Publisher | Springer Verlag |

Pages | 273-285 |

Number of pages | 13 |

ISBN (Electronic) | 3540424709 |

State | Published - 2015 |

Externally published | Yes |

Event | 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 - Berkeley, United States Duration: 18 Aug 2001 → 20 Aug 2001 |

### 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 | 2129 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 |
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Country/Territory | United States |

City | Berkeley |

Period | 18/08/01 → 20/08/01 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2001