From DNF Compression to Sunflower Theorems via Regularity

Authors Shachar Lovett, Noam Solomon, Jiapeng Zhang

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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


We thank anonymous reviewers for insightful suggestions.

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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)


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.

Subject Classification

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


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  1. Noga Alon, Amir Shpilka, and Christopher Umans. On sunflowers and matrix multiplication. computational complexity, 22(2):219-243, 2013. Google Scholar
  2. Ryan Alweiss. Personal communication, 2019. Google Scholar
  3. Paul Erdős and Richard Rado. Intersection theorems for systems of sets. Journal of the London Mathematical Society, 35(1):85-90, 1960. Google Scholar
  4. Mika Goos, Shachar Lovett, Raghu Meka, Thomas Watson, and David Zuckerman. Rectangles are nonnegative juntas. SIAM Journal on Computing, 45(5):1835-1869, 2016. Google Scholar
  5. Parikshit Gopalan, Raghu Meka, and Omer Reingold. DNF sparsification and a faster deterministic counting algorithm. Computational Complexity, 22(2):275-310, 2013. Google Scholar
  6. Alexandr V Kostochka. Extremal Problems on Δ-Systems. In Numbers, Information and Complexity, pages 143-150. Springer, 2000. Google Scholar
  7. Xin Li, Shachar Lovett, and Jiapeng Zhang. Sunflowers and Quasi-Sunflowers from Randomness Extractors. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. Google Scholar
  8. Shachar Lovett and Jiapeng Zhang. DNF sparsification beyond sunflowers. In Electronic Colloquium on Computational Complexity (ECCC), 2018. Google Scholar
  9. Alexander A Razborov. Lower bounds for the monotone complexity of some Boolean functions. In Soviet Math. Dokl., volume 31, pages 354-357, 1985. Google Scholar
  10. Benjamin Rossman. The monotone complexity of k-clique on random graphs. In Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pages 193-201. IEEE Computer Society, 2010. Google Scholar
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