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Lifting with Colourful Sunflowers

Authors Susanna F. de Rezende , Marc Vinyals

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Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Proof complexity
  • Theory of computation → Circuit complexity
Keywords
  • lifting
  • sunflower
  • clique
  • colouring
  • monotone circuit
  • cutting planes

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Abstract

We show that a generalization of the DAG-like query-to-communication lifting theorem, when proven using sunflowers over non-binary alphabets, yields lower bounds on the monotone circuit complexity and proof complexity of natural functions and formulas that are better than previously known results obtained using the approximation method. These include an n^Ω(k) lower bound for the clique function up to k ≤ n^{1/2-ε}, and an exp(Ω(n^{1/3-ε})) lower bound for a function in P.

Cite As Get BibTex

Susanna F. de Rezende and Marc Vinyals. Lifting with Colourful Sunflowers. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CCC.2025.36

Author Details

Susanna F. de Rezende
  • Lund University, Sweden
Marc Vinyals
  • University of Auckland, New Zealand

Funding

  • de Rezende, Susanna F.: Supported by Knut and Alice Wallenberg grants KAW 2018.0371 and KAW 2021.0307, ELLIIT, and the Swedish Research Council grant 2021-05104.
  • Vinyals, Marc: Supported by the Marsden Fund Council from Government funding, managed by Royal Society Te Apārangi.

Acknowledgements

We are grateful to Lukáš Folwarczný who contributed to early stages of the work, to Bruno Pasqualotto Cavalar for dicussions on the topic, and to Noah Fleming, Duri Andrea Janett, Jakob Nordström, and Shuo Pang for allowing us to include parts of their lifting theorem in the full version of this article.

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