## 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 would like to decide whether f ε ℱ or whether it differs from every g ε ℱ on more than an ε-fraction of the domain elements. The classes of functions we consider are singleton ("dictatorship") functions, monomials, and monotone disjunctive normal form 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 linear in 1/ε.

Original language | English |
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Pages (from-to) | 20-46 |

Number of pages | 27 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2003 |

Externally published | Yes |

## Keywords

- Approximation algorithms
- Boolean functions
- Property testing
- Randomized algorithms