On Block Sensitivity and Fractional Block Sensitivity

Andris Ambainis; Krišjānis Prūsis; Jevgēnijs Vihrovs

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arXiv · 1810.02393

On Block Sensitivity and Fractional Block Sensitivity

Andris Ambainis·Krišjānis Prūsis·Jevgēnijs Vihrovs

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Abstract

We investigate the relation between the block sensitivity $\text{bs}(f)$ and fractional block sensitivity $\text{fbs}(f)$ complexity measures of Boolean functions. While it is known that $\text{fbs}(f) = O(\text{bs}(f)^2)$, the best known separation achieves $\text{fbs}(f) = \left(\frac{1}{3\sqrt2} +o(1)\right) \text{bs(f)}^{3/2}$. We improve the constant factor and show a family of functions that give $\text{fbs}(f) = \left(\frac{1}{\sqrt6}-o(1)\right) \text{bs}(f)^{3/2}.$

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Andris Ambainis, Krišjānis Prūsis, Jevgēnijs Vihrovs. 2018-10-04. On Block Sensitivity and Fractional Block Sensitivity. https://arxiv.org/abs/1810.02393

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