Leakage-Resilient Hardness Equivalence to Logspace Derandomization

Shalunov, Yakov

doi:10.4230/LIPIcs.MFCS.2024.83

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Document Identifiers

DOI: 10.4230/LIPIcs.MFCS.2024.83
URN: urn:nbn:de:0030-drops-206395

Author Details

Yakov Shalunov

University of Chicago, IL, USA

Acknowledgements

Most of all, I'd like to thank Professor Chris Umans at Caltech for providing guidance and suggestions throughout this project, helping me find ways forward when I was stuck, and providing references to relevant resources. I'm also very grateful to Winter Pearson, member of the undergraduate class of 2024 at Caltech, for helping with copy-editing and proofreading.

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Yakov Shalunov. Leakage-Resilient Hardness Equivalence to Logspace Derandomization. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 83:1-83:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.MFCS.2024.83

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 equivalent to prP = prBPP. In this paper, we pursue an equivalence to derandomization of prBP⋅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 prBP⋅L, that of finding "non-no" instances of "promise search problems."

Subject Classification

ACM Subject Classification

Theory of computation → Pseudorandomness and derandomization
Theory of computation → Complexity classes

Keywords

Derandomization
logspace computation
leakage-resilient hardness
psuedorandom generators

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