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From DNF Compression to Sunflower Theorems via Regularity

Authors Shachar Lovett, Noam Solomon, Jiapeng Zhang

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Subject Classification

ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • DNF sparsification
  • sunflower conjecture
  • regular set systems

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Abstract

The sunflower conjecture is one of the most well-known open problems in combinatorics. It has several applications in theoretical computer science, one of which is DNF compression, due to Gopalan, Meka and Reingold (Computational Complexity, 2013). In this paper, we show that improved bounds for DNF compression imply improved bounds for the sunflower conjecture, which is the reverse direction of the DNF compression result. The main approach is based on regularity of set systems and a structure-vs-pseudorandomness approach to the sunflower conjecture.

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Shachar Lovett, Noam Solomon, and Jiapeng Zhang. From DNF Compression to Sunflower Theorems via Regularity. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CCC.2019.5

Author Details

Shachar Lovett
  • University of California, San Diego, CA, USA
Noam Solomon
  • MIT, Cambridge, MA, USA
Jiapeng Zhang
  • University of California, San Diego, CA, USA

Funding

  • Lovett, Shachar: Supported by NSF grant CCF-1614023.
  • Zhang, Jiapeng: Supported by NSF grant CCF-1614023.

Acknowledgements

We thank anonymous reviewers for insightful suggestions.

References

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