Lower bounds in communication complexity
T Lee, A Shraibman - Foundations and Trends® in …, 2009 - nowpublishers.com
The communication complexity of a function f (x, y) measures the number of bits that two
players, one who knows x and the other who knows y, must exchange to determine the …
players, one who knows x and the other who knows y, must exchange to determine the …
[PDF][PDF] Explicit separations between randomized and deterministic Number-on-Forehead communication
We study the power of randomness in the Number-on-Forehead (NOF) model in
communication complexity. We construct an explicit 3-player function f:[N] 3→{0, 1}, such …
communication complexity. We construct an explicit 3-player function f:[N] 3→{0, 1}, such …
An improved protocol for ExactlyN with more than 3 players
L Hambardzumyan, T Pitassi, S Sherif… - arXiv preprint arXiv …, 2023 - arxiv.org
The ExactlyN problem in the number-on-forehead (NOF) communication setting asks $ k $
players, each of whom can see every input but their own, if the $ k $ input numbers add up to …
players, each of whom can see every input but their own, if the $ k $ input numbers add up to …
Matrix multiplication and number on the forehead communication
Three-player Number On the Forehead communication may be thought of as a three-player
Number In the Hand promise model, in which each player is given the inputs that are …
Number In the Hand promise model, in which each player is given the inputs that are …
The multiparty communication complexity of set disjointness
AA Sherstov - Proceedings of the forty-fourth annual ACM symposium …, 2012 - dl.acm.org
We study the set disjointness problem in the number-on-the-forehead model of multiparty
communication.(i) We prove that k-party set disjointness has communication complexity …
communication.(i) We prove that k-party set disjointness has communication complexity …
The approximate degree of DNF and CNF formulas
AA Sherstov - Proceedings of the 54th Annual ACM SIGACT …, 2022 - dl.acm.org
The approximate degree of a Boolean function f∶{0, 1} n→{0, 1} is the minimum degree of a
real polynomial p that approximates f pointwise:| f (x)− p (x)|≤ 1/3 for all x∈{0, 1} n. For any …
real polynomial p that approximates f pointwise:| f (x)− p (x)|≤ 1/3 for all x∈{0, 1} n. For any …
Larger Corner-Free Sets from Better NOF Exactly- Protocols
N Linial, A Shraibman - arXiv preprint arXiv:2102.00421, 2021 - arxiv.org
A subset of the integer planar grid $[N]\times [N] $ is called corner-free if it contains no triple
of the form $(x, y),(x+\delta, y),(x, y+\delta) $. It is known that such a set has a vanishingly …
of the form $(x, y),(x+\delta, y),(x, y+\delta) $. It is known that such a set has a vanishingly …
A separation of NP and coNP in multiparty communication complexity
D Gavinsky, AA Sherstov - arXiv preprint arXiv:1004.0817, 2010 - arxiv.org
We prove that NP differs from coNP and coNP is not a subset of MA in the number-on-
forehead model of multiparty communication complexity for up to k=(1-\epsilon) log (n) …
forehead model of multiparty communication complexity for up to k=(1-\epsilon) log (n) …
The multiparty communication complexity of set disjointness
AA Sherstov - SIAM Journal on Computing, 2016 - SIAM
In the k-party set disjointness problem, the goal is to determine whether given subsets
S_1,S_2,\dots,S_k⊆{1,2,\dots,n\} have empty intersection. We study this problem in the …
S_1,S_2,\dots,S_k⊆{1,2,\dots,n\} have empty intersection. We study this problem in the …
On the communication complexity of high-dimensional permutations
N Linial, A Shraibman - arXiv preprint arXiv:1706.02207, 2017 - arxiv.org
We study the multiparty communication complexity of high dimensional permutations, in the
Number On the Forehead (NOF) model. This model is due to Chandra, Furst and Lipton …
Number On the Forehead (NOF) model. This model is due to Chandra, Furst and Lipton …