A simpler strong refutation of random $k$-XOR

TL;DR

This paper presents a simplified method for strong refutation of random k-XOR problems, bridging the gap between information-theoretic and computational limits with a more straightforward approach.

Contribution

It introduces a simpler algorithm and analysis for strong refutation of random k-XOR, improving understanding and potentially efficiency in this area.

Findings

Simpler algorithm for strong refutation of random k-XOR

Bridges the gap between information-theoretic and computational limits

Provides more accessible analysis compared to previous work

Abstract

Strong refutation of random CSPs is a fundamental question in theoretical computer science that has received particular attention due to the long-standing gap between the information-theoretic limit and the computational limit. This gap is recently bridged by Raghavendra, Rao and Schramm where they study sub-exponential algorithms for the regime between the two limits. In this work, we take a simpler approach to their algorithm and analysis.