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).

中文翻译：

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PNP 的查询到通信提升

我们证明了任何布尔函数 f 的 PNP 类型查询复杂度（或者，决策列表宽度）与 f 的提升版本的 PNP 类型通信复杂度呈二次关系。作为一个应用，我们展示了 Impagliazzo 和 Williams (CCC 2010) 的某个“乘积”下界方法无法捕获高达多项式因子的 PNP 通信复杂性，这回答了 Papakonstantinou、Scheder 和 Song (CCC 2014) 的问题。