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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > XIN LI:
All reports by Author Xin Li:

TR23-128 | 30th August 2023
Xue Chen, Kuan Cheng, Xin Li, Songtao Mao

Random Shortening of Linear Codes and Application

Random linear codes (RLCs) are well known to have nice combinatorial properties and near-optimal parameters in many different settings. However, getting explicit constructions matching the parameters of RLCs is challenging, and RLCs are hard to decode efficiently. This motivated several previous works to study the problem of partially derandomizing RLCs, ... more >>>


TR23-058 | 23rd April 2023
Xin Li, Yan Zhong

Explicit Directional Affine Extractors and Improved Hardness for Linear Branching Programs

Affine extractors give some of the best-known lower bounds for various computational models, such as AC$^0$ circuits, parity decision trees, and general Boolean circuits. However, they are not known to give strong lower bounds for read-once branching programs (ROBPs). In a recent work, Gryaznov, Pudl\'{a}k, and Talebanfard (CCC' 22) introduced ... more >>>


TR22-082 | 27th May 2022
Omar Alrabiah, Eshan Chattopadhyay, Jesse Goodman, Xin Li, João Ribeiro

Low-Degree Polynomials Extract from Local Sources

We continue a line of work on extracting random bits from weak sources that are generated by simple processes. We focus on the model of locally samplable sources, where each bit in the source depends on a small number of (hidden) uniformly random input bits. Also known as local sources, ... more >>>


TR20-060 | 23rd April 2020
Eshan Chattopadhyay, Jesse Goodman, Vipul Goyal, Xin Li

Leakage-Resilient Extractors and Secret-Sharing against Bounded Collusion Protocols

In a recent work, Kumar, Meka, and Sahai (FOCS 2019) introduced the notion of bounded collusion protocols (BCPs), in which $N$ parties wish to compute some joint function $f:(\{0,1\}^n)^N\to\{0,1\}$ using a public blackboard, but such that only $p$ parties may collude at a time. This generalizes well studied models in ... more >>>


TR19-184 | 13th December 2019
Eshan Chattopadhyay, Jesse Goodman, Vipul Goyal, Xin Li

Extractors for Adversarial Sources via Extremal Hypergraphs

Randomness extraction is a fundamental problem that has been studied for over three decades. A well-studied setting assumes that one has access to multiple independent weak random sources, each with some entropy. However, this assumption is often unrealistic in practice. In real life, natural sources of randomness can produce samples ... more >>>


TR18-082 | 21st April 2018
Xin Li, Shachar Lovett, Jiapeng Zhang

Sunflowers and Quasi-sunflowers from Randomness Extractors

The Erdos-Rado sunflower theorem (Journal of Lond. Math. Soc. 1960) is a fundamental result in combinatorics, and the corresponding sunflower conjecture is a central open problem. Motivated by applications in complexity theory, Rossman (FOCS 2010) extended the result to quasi-sunflowers, where similar conjectures emerge about the optimal parameters for which ... more >>>


TR15-075 | 29th April 2015
Eshan Chattopadhyay, Vipul Goyal, Xin Li

Non-Malleable Extractors and Codes, with their Many Tampered Extensions

Revisions: 1

Randomness extractors and error correcting codes are fundamental objects in computer science. Recently, there have been several natural generalizations of these objects, in the context and study of tamper resilient cryptography. These are \emph{seeded non-malleable extractors}, introduced by Dodis and Wichs \cite{DW09}; \emph{seedless non-malleable extractors}, introduced by Cheraghchi and Guruswami ... more >>>


TR14-149 | 10th November 2014
Kai-Min Chung, Xin Li, Xiaodi Wu

Multi-Source Randomness Extractors Against Quantum Side Information, and their Applications

We study the problem of constructing multi-source extractors in the quantum setting, which extract almost uniform random bits against quantum side information collected from several initially independent classical random sources. This is a natural generalization of seeded randomness extraction against quantum side information and classical independent source extraction. With new ... more >>>




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