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Sensitivity Versus Certificate Complexity of Boolean Functions

  • Andris Ambainis
  • Krišjānis Prūsis
  • Jevgēnijs VihrovsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)

Abstract

Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been notoriously hard to obtain even exponential bounds. Since block sensitivity is known to be polynomially related to certificate complexity, an equivalent of proving this conjecture would be showing that the certificate complexity is polynomially related to sensitivity. Previously, it has been shown that \(bs(f) \le C(f) \le 2^{s(f)-1} s(f) - (s(f)-1)\). In this work, we give a better upper bound of \(bs(f) \le C(f) \le \max \left( 2^{s(f)-1}\left( s(f)-\frac{1}{3}\right) , s(f)\right) \) using a recent theorem limiting the structure of function graphs. We also examine relations between these measures for functions with 1-sensitivity \(s_1(f)=2\) and arbitrary 0-sensitivity \(s_0(f)\).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Krišjānis Prūsis
    • 1
  • Jevgēnijs Vihrovs
    • 1
    Email author
  1. 1.Faculty of ComputingUniversity of LatviaRīgaLatvia

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