### Abstract

A Boolean function f : (0, 1)n (0, 1) is called a dictator if it depends on exactly one variable i.e f(x1, x2, . . ., xn) = xi for some i (n). In this work, we study a k-query dictatorship test. Dictatorship tests are central in proving many hardness results for constraint satisfaction problems. The dictatorship test is said to have perfect completeness if it accepts any dictator function. The soundness of a test is the maximum probability with which it accepts any function far from a dictator. Our main result is a k-query dictatorship test with perfect completeness and soundness 2k 2 +1 k, where k is of the form 2t-1 for any integer t 2. This improves upon the result of (25) which gave a dictatorship test with soundness 2k 2 +3 k.

Original language | English (US) |
---|---|

Title of host publication | 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017 |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Volume | 93 |

ISBN (Electronic) | 9783959770552 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017 - Kanpur, India Duration: Dec 12 2017 → Dec 14 2017 |

### Other

Other | 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017 |
---|---|

Country | India |

City | Kanpur |

Period | 12/12/17 → 12/14/17 |

### Fingerprint

### Keywords

- Distatorship Test
- Fourier Analysis
- Property Testing

### ASJC Scopus subject areas

- Software

### Cite this

*37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017*(Vol. 93). [15] Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.FSTTCS.2017.15

**An improved dictatorship test with perfect completeness.** / Bhangale, Amey; Khot, Subhash; Thiruvenkatachari, Devanathan.

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

*37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017.*vol. 93, 15, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017, Kanpur, India, 12/12/17. https://doi.org/10.4230/LIPIcs.FSTTCS.2017.15

}

TY - GEN

T1 - An improved dictatorship test with perfect completeness

AU - Bhangale, Amey

AU - Khot, Subhash

AU - Thiruvenkatachari, Devanathan

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A Boolean function f : (0, 1)n (0, 1) is called a dictator if it depends on exactly one variable i.e f(x1, x2, . . ., xn) = xi for some i (n). In this work, we study a k-query dictatorship test. Dictatorship tests are central in proving many hardness results for constraint satisfaction problems. The dictatorship test is said to have perfect completeness if it accepts any dictator function. The soundness of a test is the maximum probability with which it accepts any function far from a dictator. Our main result is a k-query dictatorship test with perfect completeness and soundness 2k 2 +1 k, where k is of the form 2t-1 for any integer t 2. This improves upon the result of (25) which gave a dictatorship test with soundness 2k 2 +3 k.

AB - A Boolean function f : (0, 1)n (0, 1) is called a dictator if it depends on exactly one variable i.e f(x1, x2, . . ., xn) = xi for some i (n). In this work, we study a k-query dictatorship test. Dictatorship tests are central in proving many hardness results for constraint satisfaction problems. The dictatorship test is said to have perfect completeness if it accepts any dictator function. The soundness of a test is the maximum probability with which it accepts any function far from a dictator. Our main result is a k-query dictatorship test with perfect completeness and soundness 2k 2 +1 k, where k is of the form 2t-1 for any integer t 2. This improves upon the result of (25) which gave a dictatorship test with soundness 2k 2 +3 k.

KW - Distatorship Test

KW - Fourier Analysis

KW - Property Testing

UR - http://www.scopus.com/inward/record.url?scp=85043997421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043997421&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.FSTTCS.2017.15

DO - 10.4230/LIPIcs.FSTTCS.2017.15

M3 - Conference contribution

VL - 93

BT - 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -