Disordered systems insights on computational hardness
D Gamarnik, C Moore… - Journal of Statistical …, 2022 - iopscience.iop.org
In this review article we discuss connections between the physics of disordered systems,
phase transitions in inference problems, and computational hardness. We introduce two …
phase transitions in inference problems, and computational hardness. We introduce two …
Lossy cryptography from code-based assumptions
Over the past few decades, we have seen a proliferation of advanced cryptographic
primitives with lossy or homomorphic properties built from various assumptions such as …
primitives with lossy or homomorphic properties built from various assumptions such as …
A near-cubic lower bound for 3-query locally decodable codes from semirandom CSP refutation
A code C∶{0, 1} k→{0, 1} n is aq-locally decodable code (q-LDC) if one can recover any
chosen bit bi of the message b∈{0, 1} k with good confidence by randomly querying the …
chosen bit bi of the message b∈{0, 1} k with good confidence by randomly querying the …
[PDF][PDF] An exponential lower bound for linear 3-query locally correctable codes
PK Kothari, P Manohar - Proceedings of the 56th Annual ACM …, 2024 - dl.acm.org
We prove that the blocklength n of a linear 3-query locally correctable code (LCC) L∶ F k→
F n with distance δ must be at least n≥ 2Ω ((δ2 k/(| F|− 1) 2) 1/8). In particular, the …
F n with distance δ must be at least n≥ 2Ω ((δ2 k/(| F|− 1) 2) 1/8). In particular, the …
Efficient Algorithms for Semirandom Planted CSPs at the Refutation Threshold
We present an efficient algorithm to solve semirandom planted instances of any Boolean
constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst …
constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst …
A simple and sharper proof of the hypergraph Moore bound
The hypergraph Moore bound characterizes the extremal trade-off between the girth—the
number of hyperedges in the smallest cycle or even cover (a subhypergraph with all …
number of hyperedges in the smallest cycle or even cover (a subhypergraph with all …
Exponential lower bounds for smooth 3-LCCs and sharp bounds for designs
PK Kothari, P Manohar - 2024 IEEE 65th Annual Symposium …, 2024 - ieeexplore.ieee.org
We give improved lower bounds for binary 3-query locally correctable codes (3-LCCs)
C:{\0,1\}^k→{\0,1\}^n. Specifically, we prove: 1) If C is a linear design 3-LCC, then n≧2^(1 …
C:{\0,1\}^k→{\0,1\}^n. Specifically, we prove: 1) If C is a linear design 3-LCC, then n≧2^(1 …
A near-linear time approximation algorithm for beyond-worst-case graph clustering
We consider the semi-random graph model of [Makarychev, Makarychev and
Vijayaraghavan, STOC'12], where, given a random bipartite graph with $\alpha $ edges and …
Vijayaraghavan, STOC'12], where, given a random bipartite graph with $\alpha $ edges and …
Algorithms for Sparse LPN and LSPN Against Low-noise
X Chen, W Shu, Z Zhou - arXiv preprint arXiv:2407.19215, 2024 - arxiv.org
We study learning algorithms for two sparse variants of the classical learning parity with
noise (LPN) problem. We provide a new algorithmic framework that improves the state of the …
noise (LPN) problem. We provide a new algorithmic framework that improves the state of the …
A Geometric Perspective on the Injective Norm of Sums of Random Tensors
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine
inequality, have been an important tool in both applied and pure mathematics. We study …
inequality, have been an important tool in both applied and pure mathematics. We study …