Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem

Cited by: 0|Bibtex|Views4|Links

Abstract:

Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, $\bullet \quad \mathrm{deg}(f) = O(\widetilde{\mathrm{deg}}(f)^2)$: The degree of $f$ is at most quadratic in the approximate degree of $f$. This is optimal as witnessed by the OR function. $\bullet \quad \mathrm{D}(f) = O(\mathrm{Q}(f...More

Code:

Data:

Your rating :
0

 

Tags
Comments