Leakage-Resilient Hardness Equivalence to Logspace Derandomization

Yakov Shalunov

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arXiv · 2312.14023

Leakage-Resilient Hardness Equivalence to Logspace Derandomization

Yakov Shalunov

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Abstract

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.''

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Yakov Shalunov. 2023-12-21. Leakage-Resilient Hardness Equivalence to Logspace Derandomization. https://arxiv.org/abs/2312.14023

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