Revision #1 Authors: Mika Göös, Pritish Kamath, Toniann Pitassi, Thomas Watson

Accepted on: 3rd December 2018 02:09

Downloads: 597

Keywords:

We prove that the $\text{P}^{\small\text{NP}}$-type query complexity (alternatively, decision list width) of any boolean function $f$ is quadratically related to the $\text{P}^{\small\text{NP}}$-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 $\text{P}^{\small\text{NP}}$ communication complexity up to polynomial factors, which answers a question of Papakonstantinou, Scheder, and Song (CCC 2014).

TR17-024 Authors: Mika Göös, Pritish Kamath, Toniann Pitassi, Thomas Watson

Publication: 16th February 2017 13:30

Downloads: 1722

Keywords:

We prove that the $\text{P}^{\small\text{NP}}$-type query complexity (alternatively, decision list width) of any boolean function $f$ is quadratically related to the $\text{P}^{\small\text{NP}}$-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 $\text{P}^{\small\text{NP}}$ communication complexity up to polynomial factors, which answers a question of Papakonstantinou, Scheder, and Song (CCC 2014).