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REPORTS > KEYWORD > FOURIER WEIGHT OF DECISION TREES:
Reports tagged with Fourier weight of decision trees:
TR20-128 | 3rd September 2020
Alexander A. Sherstov, Andrey Storozhenko, Pei Wu

An Optimal Separation of Randomized and Quantum Query Complexity

We prove that for every decision tree, the absolute values of the Fourier coefficients of given order $\ell\geq1$ sum to at most $c^{\ell}\sqrt{{d\choose\ell}(1+\log n)^{\ell-1}},$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant. This bound is essentially tight and settles a ... more >>>




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