On Block Sensitivity and Fractional Block Sensitivity

10/04/2018

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by   Andris Ambainis, et al.

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We investigate the relation between the block sensitivity bs(f) and fractional block sensitivity fbs(f) complexity measures of Boolean functions. While it is known that fbs(f) = O(bs(f)^2), the best known separation achieves fbs(f) = (1/3√(2) +o(1)) bs(f)^3/2. We improve the constant factor and show a family of functions that give fbs(f) = (1/√(6)-o(1)) bs(f)^3/2.