This paper uses structural complexity theory to study whether there is a chasm between knowing an object exists and getting one's hands on the object or its properties. In particular, we study the nontransparency of backbones. We show that, under the widely believed assumption that integer factoring is hard, there exist sets of boolean formulas that have obvious, nontrivial backbones yet finding the values of those backbones is intractable. We also show that, under the same assumption, there exist sets of boolean formulas that obviously have large backbones yet producing such a backbone is intractable. Furthermore, we show that if integer factoring is not merely worst-case hard but is frequently hard, as is widely believed, then the frequency of hardness in our two results is not too much less than that frequency. These results hold even if one's assumptions are, respectively, $\mathrm{P}\ne \mathrm{NP}\cap \mathrm{coNP}$ or that some $\mathrm{NP}\cap \mathrm{coNP}$ problem is frequently hard.

本文使用结构复杂性理论来研究在知道一个对象存在与接触到该对象或其属性之间是否存在鸿沟。我们特别研究了主干的非透明性。我们表明，在普遍认为整数因子分解很难的假设下，存在多组布尔公式，这些公式具有明显的、非平凡的主干，但找到这些主干的值却很困难。我们还表明，在相同的假设下，存在明显具有大主干的布尔公式集，但产生这样的主干是难以处理的。此外，我们表明，如果整数因子分解不仅是最坏情况下的困难，而且经常是困难的，正如人们普遍认为的那样，那么我们两个结果中的困难频率不会比该频率小太多。$\mathrm{磷}\ne \mathrm{NP}\cap \mathrm{联合NP}$ 或者说一些 $\mathrm{NP}\cap \mathrm{联合NP}$ 问题往往很难。