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A Majority Lemma for Randomised Query Complexity

Authors Mika Göös, Gilbert Maystre

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Author Details

Mika Göös
  • School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland
Gilbert Maystre
  • School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland

Acknowledgements

We thank Thomas Watson and anonymous reviewers for helpful comments.

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Mika Göös and Gilbert Maystre. A Majority Lemma for Randomised Query Complexity. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CCC.2021.18

Abstract

We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj∘gⁿ) = Θ(n⋅R ̅_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f∘gⁿ, it suffices to prove a sufficiently strong form of the result only in the special case g = GapOr.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Query Complexity
  • Composition
  • Majority

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