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New Constructions with Quadratic Separation between Sensitivity and Block Sensitivity

Authors Siddhesh Chaubal, Anna Gál

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Siddhesh Chaubal
  • University of Texas at Austin, USA
Anna Gál
  • University of Texas at Austin, USA

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Siddhesh Chaubal and Anna Gál. New Constructions with Quadratic Separation between Sensitivity and Block Sensitivity. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSTTCS.2018.13

Abstract

Nisan and Szegedy [Nisan and Szegedy, 1994] conjectured that block sensitivity is at most polynomial in sensitivity for any Boolean function. There is a huge gap between the best known upper bound on block sensitivity in terms of sensitivity - which is exponential, and the best known separating examples - which give only a quadratic separation between block sensitivity and sensitivity. In this paper we give various new constructions of families of Boolean functions that exhibit quadratic separation between sensitivity and block sensitivity. Our constructions have several novel aspects. For example, we give the first direct constructions of families of Boolean functions that have both 0-block sensitivity and 1-block sensitivity quadratically larger than sensitivity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
Keywords
  • Sensitivity Conjecture
  • Boolean Functions
  • Complexity Measures

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References

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