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Query-to-Communication Lifting for PNP


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).

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  • 06 April 2019

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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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Correspondence to Thomas Watson.

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The original version of this article was revised: The inline images were not processed in the original version and updated here

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Göös, M., Kamath, P., Pitassi, T. et al. Query-to-Communication Lifting for PNP. comput. complex. 28, 113–144 (2019).

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  • Query
  • Communication
  • Lifting
  • P NP

Subject classification

  • 68Q15