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computational complexity

, Volume 28, Issue 1, pp 113–144 | Cite as

Query-to-Communication Lifting for PNP

  • Mika Göös
  • Pritish Kamath
  • Toniann Pitassi
  • Thomas WatsonEmail author
Article
  • 15 Downloads

Abstract

We prove that the PNP-type query complexity (alternatively, decision list width) of any Boolean function f is quadratically related to the PNP-type communication complexity of a lifted version of f. As an application, we show that a certain “product” lower bound method of Impagliazzo and Williams (CCC 2010) fails to capture PNP communication complexity up to polynomial factors, which answers a question of Papakonstantinou, Scheder, and Song (CCC 2014).

Keywords

Query Communication Lifting PNP 

Subject classification

68Q15 

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Notes

Acknowledgements

We thank anonymous reviewers for comments, especially for a suggestion that led to a simplified proof of Claim 3.6. We thank Paul Balister, Shalev Ben-David, Béla Bollobás, Robin Kothari, Nirman Kumar, Santosh Kumar, Govind Ramnarayan, Madhu Sudan, Li-Yang Tan, and Justin Thaler for discussions and correspondence. T.W. was supported by NSF grant CCF-1657377. A preliminary version of this work was published as Göös et al. (2017).

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Copyright information

© Springer Nature Switzerland AG 2018
corrected publication 2019

Authors and Affiliations

  • Mika Göös
    • 1
  • Pritish Kamath
    • 2
  • Toniann Pitassi
    • 3
  • Thomas Watson
    • 4
    Email author
  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.University of TorontoTorontoCanada
  4. 4.University of MemphisMemphisUSA

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