An improved dictatorship test with perfect completeness

Amey Bhangale, Subhash Khot, Devanathan Thiruvenkatachari

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
EditorsSatya Lokam, R. Ramanujam
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770552
DOIs
StatePublished - Jan 1 2018
Event37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017 - Kanpur, India
Duration: Dec 12 2017Dec 14 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume93
ISSN (Print)1868-8969

Other

Other37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
CountryIndia
CityKanpur
Period12/12/1712/14/17

Keywords

  • Distatorship Test
  • Fourier Analysis
  • Property Testing

ASJC Scopus subject areas

  • Software

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  • Cite this

    Bhangale, A., Khot, S., & Thiruvenkatachari, D. (2018). An improved dictatorship test with perfect completeness. In S. Lokam, & R. Ramanujam (Eds.), 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017 [15] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 93). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.FSTTCS.2017.15