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 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是复杂性理论中的一个目标，Yanyi Liu和Rafael Pass的最新重要成果确定了一类新的硬度假设，在此假设下可以有效执行时间有界去随机化：即“泄漏弹性硬度”。他们确定了该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，寻求与$\mathsf{prBP{\cdot}L}$（具有双向随机性的对数空间承诺问题）去随机化的等价性。我们能够获得类似的“泄漏弹性硬度”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。