We study the relations between the notions of highness, lowness and logical depth in the setting of complexity theory. We introduce a new notion of polylog depth based on time bounded Kolmogorov complexity. We show polylog depth satisfies all basic logical depth properties, namely sets in P are not polylog deep, sets with (time bounded)-Kolmogorov complexity greater than polylog are not polylog deep, and only polylog deep sets can polynomially Turing compute a polylog deep set. We prove that if NP does not have p-measure zero, then NP contains polylog deep sets. We show that every high set for E contains a polylog deep set in its polynomial Turing degree, and that there exist $\mathrm{Low}(\mathrm{E},\mathrm{EXP})$ polylog deep sets. Keywords: algorithmic information theory; Kolmogorov complexity; Bennett logical depth.

我们在复杂性理论的背景下研究了高级，低级和逻辑深度之间的关系。我们引入了基于时间限制的Kolmogorov复杂度的多测井深度的新概念。我们显示polylog深度满足所有基本逻辑深度属性，即P中的集合不是polylog的深层，（时间限制）-Kolmogorov复杂度大于polylog的集合不是polylog的深层，并且只有polylog的深集可以多项式图灵计算出polylog的深集。我们证明，如果NP不具有p -measure零，则NP包含多对数深集。我们表明，E的每个高集在其多项式图灵度中都包含一个多对数深集，并且存在$\mathrm{低}（\mathrm{Ë}，\mathrm{经验值}）$polylog深集。关键词：算法信息论 Kolmogorov的复杂性；贝内特的逻辑深度。