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A Simpler Strong Refutation of Random k-XOR

Author Kwangjun Ahn

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Kwangjun Ahn
  • Department of EECS, Massachusetts Institute of Technology, Cambridge, MA, USA


The author thanks Vijay Bhattiprolu for suggesting the idea of re-scaling entries of the matrix representation for simpler refutation algorithm. The author also thanks anonymous reviewers for various comments that indeed help the author improve the presentation.

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Kwangjun Ahn. A Simpler Strong Refutation of Random k-XOR. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 2:1-2:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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 algorithms and analyses.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Strong refutation
  • Random k-XOR
  • Spectral method
  • Trace power method


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