Leakage-Resilient Hardness Equivalence to Logspace Derandomization

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1. Verfasser: Shalunov, Yakov
Format: Preprint
Veröffentlicht: 2023
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_version_ 1866914850776547328
author Shalunov, Yakov
author_facet Shalunov, Yakov
contents 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.''
format Preprint
id arxiv_https___arxiv_org_abs_2312_14023
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Leakage-Resilient Hardness Equivalence to Logspace Derandomization
Shalunov, Yakov
Computational Complexity
68Q15 (Primary) 68Q25, 68Q87 (Secondary)
F.1.3; G.3
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.''
title Leakage-Resilient Hardness Equivalence to Logspace Derandomization
topic Computational Complexity
68Q15 (Primary) 68Q25, 68Q87 (Secondary)
F.1.3; G.3
url https://arxiv.org/abs/2312.14023