Zobrazeno 1 - 10
of 185
pro vyhledávání: '"Khot, Subhash"'
We prove local and global inverse theorems for general $3$-wise correlations over pairwise-connected distributions. Let $\mu$ be a distribution over $\Sigma \times \Gamma \times \Phi$ such that the supports of $\mu_{xy}$, $\mu_{xz}$, and $\mu_{yz}$ a
Externí odkaz:
http://arxiv.org/abs/2411.15133
We prove that any subset $A \subseteq [3]^n$ with $3^{-n}|A| \ge (\log\log\log\log n)^{-c}$ contains a combinatorial line of length $3$, i.e., $x, y, z \in A$, not all equal, with $x_i=y_i=z_i$ or $(x_i,y_i,z_i)=(0,1,2)$ for all $i = 1, 2, \dots, n$.
Externí odkaz:
http://arxiv.org/abs/2411.15137
We propose a framework of algorithm vs. hardness for all Max-CSPs and demonstrate it for a large class of predicates. This framework extends the work of Raghavendra [STOC, 2008], who showed a similar result for almost satisfiable Max-CSPs. Our framew
Externí odkaz:
http://arxiv.org/abs/2408.15377
In a $3$-$\mathsf{XOR}$ game $\mathcal{G}$, the verifier samples a challenge $(x,y,z)\sim \mu$ where $\mu$ is a probability distribution over $\Sigma\times\Gamma\times\Phi$, and a map $t\colon \Sigma\times\Gamma\times\Phi\to\mathcal{A}$ for a finite
Externí odkaz:
http://arxiv.org/abs/2408.09352
We study parallel repetition of k-player games where the constraints satisfy the projection property. We prove exponential decay in the value of a parallel repetition of projection games with value less than 1.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/2312.04783
For a prime $p$, a restricted arithmetic progression in $\mathbb{F}_p^n$ is a triplet of vectors $x, x+a, x+2a$ in which the common difference $a$ is a non-zero element from $\{0,1,2\}^n$. What is the size of the largest $A\subseteq \mathbb{F}_p^n$ t
Externí odkaz:
http://arxiv.org/abs/2308.06600
We prove a stability result for general $3$-wise correlations over distributions satisfying mild connectivity properties. More concretely, we show that if $\Sigma,\Gamma$ and $\Phi$ are alphabets of constant size, and $\mu$ is a pairwise connected di
Externí odkaz:
http://arxiv.org/abs/2307.16248
We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive
Externí odkaz:
http://arxiv.org/abs/2211.13741
We show improved monotonicity testers for the Boolean hypercube under the $p$-biased measure, as well as over the hypergrid $[m]^n$. Our results are: 1. For any $p\in (0,1)$, for the $p$-biased hypercube we show a non-adaptive tester that makes $\til
Externí odkaz:
http://arxiv.org/abs/2211.09229
Autor:
S., Karthik C., Khot, Subhash
The k-Clique problem is a canonical hard problem in parameterized complexity. In this paper, we study the parameterized complexity of approximating the k-Clique problem where an integer k and a graph G on n vertices are given as input, and the goal i
Externí odkaz:
http://arxiv.org/abs/2112.03983