The present work argues that strong arithmetic circuit lower bounds yield Boolean circuit lower bounds. In particular we show that the De Morgan Boolean formula complexity upper-bounds algebraic variants of the Kolomogorov complexity measure of partial differential incarnations of Turing machines. We devise from this connection new non-trivial upper and lower bounds for the De Morgan Boolean formula complexity of some familiar Boolean functions.

翻译：目前的工作认为,强大的算术电路下界使得Boolean电路下界变得低界,特别是,我们表明,De Morgan Boolean 公式复杂程度高界代数变体是Kolomogorov对图灵机器部分不同化的复杂度的局部代数。我们从这个联系中设计出一些熟悉布林功能的De Morgan Boolean 公式复杂程度的非三界上界和下界。