Abstract
We give a structure theorem for Boolean functions on the biased hypercube which are -close to degree~d in L2, showing that they are close to \emph{sparse juntas}.
Our structure theorem implies that such functions are O(Cd+p)-close to constant functions. We pinpoint the exact value of the constant Cd.
The earlier version is under the title: "Low degree almost Boolean functions are sparse juntas".
Our structure theorem implies that such functions are O(Cd+p)-close to constant functions. We pinpoint the exact value of the constant Cd.
The earlier version is under the title: "Low degree almost Boolean functions are sparse juntas".
| Original language | English |
|---|---|
| Article number | TR17-180 |
| Number of pages | 24 |
| Journal | Electronic colloquium on computational complexity ECCC ; research reports, surveys and books in computational complexity |
| State | Published - 26 Nov 2017 |