Efficient derandomization has long been a goal in complexity theory, and a major recent result by Yanyi Liu and Rafael Pass identifies a new class of hardness assumption under which it is possible to perform time-bounded derandomization efficiently: that of ''leakage-resilient hardness.'' They identify a specific form of this assumption which is $\textit{equivalent}$ to $\mathsf{prP} = \mathsf{prBPP}$. In this paper, we pursue a an equivalence to derandomization of $\mathsf{prBP{\cdot}L}$ (logspace promise problems with two-way randomness) through techniques analogous to Liu and Pass. We are able to obtain an equivalence between a similar ''leakage-resilient hardness'' assumption and a slightly stronger statement than derandomization of $\mathsf{prBP{\cdot}L}$, that of finding ''non-no'' instances of ''promise search problems.''

翻译：高效去随机化长期以来一直是复杂性理论中的一个目标，而Yanyi Liu和Rafael Pass近期的一项重大成果识别出一类新的硬度假设，在该假设下可以高效执行时间有界去随机化：即“抗泄漏硬度”。他们确定了这一假设的一种特定形式，该形式等价于$\mathsf{prP} = \mathsf{prBPP}$。在本文中，我们通过类似于Liu和Pass的技术，致力于建立与$\mathsf{prBP{\cdot}L}$（具有两方随机性的对数空间承诺问题）的去随机化之间的等价关系。我们能够获得一个类似的“抗泄漏硬度”假设与一个比$\mathsf{prBP{\cdot}L}$去随机化稍强的陈述之间的等价性，即寻找“承诺搜索问题”的“非否”实例。