Query-to-Communication Lifting for P NP
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).
Göös, M., Kamath, P., Pitassi, T., & Watson, T. (2019). Query-to-Communication Lifting for P NP. Computational Complexity, 28 (1), 113-144. https://doi.org/10.1007/s00037-018-0175-5