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Sensitivity, certificate complexity and block sensitivity are widely usedBoolean function complexity measures. A longstanding open problem, proposed byNisan and Szegedy, is whether sensitivity and block sensitivity arepolynomially related. Motivated by the constructions of functions which achievethe largest known separations, we study the relation between 1-certificatecomplexity and 0-sensitivity and 0-block sensitivity.  Previously the best known lower bound was $C_1(f)\geq \frac{bs_0(f)}{2s_0(f)}$, achieved by Kenyon and Kutin. We improve this to $C_1(f)\geq \frac{3bs_0(f)}{2 s_0(f)}$. While this improvement is only by a constant factor, thisis quite important, as it precludes achieving a superquadratic separationbetween $bs(f)$ and $s(f)$ by iterating functions which reach this bound. Inaddition, this bound is tight, as it matches the construction of Ambainis andSun up to an additive constant.

A Tight Lower Bound on Certificate Complexity in Terms of Block Sensitivity and Sensitivity