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Query-to-Communication Lifting for P^NP

Authors Mika Göös, Pritish Kamath, Toniann Pitassi, Thomas Watson

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Mika Göös
Pritish Kamath
Toniann Pitassi
Thomas Watson

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Mika Göös, Pritish Kamath, Toniann Pitassi, and Thomas Watson. Query-to-Communication Lifting for P^NP. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CCC.2017.12

Abstract

We prove that the P^NP-type query complexity (alternatively, decision list width) of any boolean function f is quadratically related to the P^NP-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 P^NP communication complexity up to polynomial factors, which answers a question of Papakonstantinou, Scheder, and Song (CCC 2014).
Keywords
  • Communication Complexity
  • Query Complexity
  • Lifting Theorem
  • P^NP

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