Log-rank and lifting for AND-functions
Let f:{0, 1} n→{0, 1} be a boolean function, and let f∧(x, y)= f (x∧ y) denote the AND-function
of f, where x∧ y denotes bit-wise AND. We study the deterministic communication …
of f, where x∧ y denotes bit-wise AND. We study the deterministic communication …
Complexity measures on the symmetric group and beyond
We extend the definitions of complexity measures of functions to domains such as the
symmetric group. The complexity measures we consider include degree, approximate …
symmetric group. The complexity measures we consider include degree, approximate …
Low-degree learning and the metric entropy of polynomials
A Eskenazis, P Ivanisvili, L Streck - arXiv preprint arXiv:2203.09659, 2022 - arxiv.org
Let $\mathscr {F} _ {n, d} $ be the class of all functions $ f:\{-1, 1\}^ n\to [-1, 1] $ on the $ n $-
dimensional discrete hypercube of degree at most $ d $. In the first part of this paper, we …
dimensional discrete hypercube of degree at most $ d $. In the first part of this paper, we …
Degree 2 Boolean functions on Grassmann graphs
J De Beule, J D'haeseleer, F Ihringer… - arXiv preprint arXiv …, 2022 - arxiv.org
We investigate the existence of Boolean degree $ d $ functions on the Grassmann graph of
$ k $-spaces in the vector space $\mathbb {F} _q^ n $. For $ d= 1$ several non-existence …
$ k $-spaces in the vector space $\mathbb {F} _q^ n $. For $ d= 1$ several non-existence …
Junta threshold for low degree Boolean functions on the slice
Y Filmus - arXiv preprint arXiv:2203.04760, 2022 - arxiv.org
arXiv:2203.04760v2 [math.CO] 14 Mar 2022 Page 1 arXiv:2203.04760v2 [math.CO] 14 Mar
2022 Junta threshold for low degree Boolean functions on the slice Yuval Filmus March 15 …
2022 Junta threshold for low degree Boolean functions on the slice Yuval Filmus March 15 …
Analyzing Boolean functions on the biased hypercube via higher-dimensional agreement tests
We propose a new paradigm for studying the structure of Boolean functions on the biased
Boolean hypercube, ie when the measure is µp and p is potentially very small, eg as small …
Boolean hypercube, ie when the measure is µp and p is potentially very small, eg as small …
Relationships between the number of inputs and other complexity measures of Boolean functions
J Wellens - arXiv preprint arXiv:2005.00566, 2020 - arxiv.org
We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove
new bounds on the number of relevant variables for boolean functions in terms of a variety of …
new bounds on the number of relevant variables for boolean functions in terms of a variety of …
A structure theorem for almost low-degree functions on the slice
Abstract The Fourier-Walsh expansion of a Boolean function f: 0, 1 n→ 0, 1 is its unique
representation as a multilinear polynomial. The Kindler-Safra theorem (2002) asserts that if …
representation as a multilinear polynomial. The Kindler-Safra theorem (2002) asserts that if …
On degree-3 and (n− 4)-correlation-immune perfect colorings of n-cubes
DS Krotov, AA Valyuzhenich - Discrete Mathematics, 2024 - Elsevier
A perfect k-coloring of the Boolean hypercube Q n is a function from the set of binary words
of length n onto a k-set of colors such that for any colors i and j every word of color i has …
of length n onto a k-set of colors such that for any colors i and j every word of color i has …
Assorted results in boolean function complexity, uniform sampling and clique partitions of graphs
JJL Wellens - 2020 - dspace.mit.edu
This thesis consists of three disparate parts. In the first, we generalize and extend recent
ideas of Chiarelli, Hatami and Saks to obtain new bounds on the number of relevant …
ideas of Chiarelli, Hatami and Saks to obtain new bounds on the number of relevant …