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Lifting with Sunflowers

Authors Shachar Lovett, Raghu Meka, Ian Mertz, Toniann Pitassi, Jiapeng Zhang

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Author Details

Shachar Lovett
  • Department of Computer Science, University of California San Diego, CA, USA
Raghu Meka
  • Department of Computer Science, University of California Los Angeles, CA, USA
Ian Mertz
  • Department of Computer Science, University of Toronto, Canada
Toniann Pitassi
  • Department of Computer Science, University of Toronto, Canada
  • Department of Mathematics, Institute for Advanced Study, Princeton, NJ, USA
Jiapeng Zhang
  • Department of Computer Science, University of Southern California, Los Angeles, CA, USA

Funding

  • Lovett, Shachar: Research supported by NSF Award DMS-1953928.
  • Mertz, Ian: Research supported by NSERC.
  • Pitassi, Toniann: Research supported by NSF Award CCF-1900460 and NSERC.

Acknowledgements

The authors thank Paul Beame for comments.

Cite As Get BibTex

Shachar Lovett, Raghu Meka, Ian Mertz, Toniann Pitassi, and Jiapeng Zhang. Lifting with Sunflowers. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 104:1-104:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ITCS.2022.104

Abstract

Query-to-communication lifting theorems translate lower bounds on query complexity to lower bounds for the corresponding communication model. In this paper, we give a simplified proof of deterministic lifting (in both the tree-like and dag-like settings). Our proof uses elementary counting together with a novel connection to the sunflower lemma. 
In addition to a simplified proof, our approach opens up a new avenue of attack towards proving lifting theorems with improved gadget size - one of the main challenges in the area. Focusing on one of the most widely used gadgets - the index gadget - existing lifting techniques are known to require at least a quadratic gadget size. Our new approach combined with robust sunflower lemmas allows us to reduce the gadget size to near linear. We conjecture that it can be further improved to polylogarithmic, similar to the known bounds for the corresponding robust sunflower lemmas.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Theory of computation → Communication complexity
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Circuit complexity
  • Theory of computation → Proof complexity
Keywords
  • Lifting theorems
  • communication complexity
  • combinatorics
  • sunflowers

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