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DOI: 10.4230/LIPIcs.MFCS.2024.83

Leakage-Resilient Hardness Equivalence to Logspace Derandomization

Authors: Yakov Shalunov

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

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."

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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)

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@InProceedings{shalunov:LIPIcs.MFCS.2024.83,
  author =	{Shalunov, Yakov},
  title =	{{Leakage-Resilient Hardness Equivalence to Logspace Derandomization}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{83:1--83:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.83},
  URN =		{urn:nbn:de:0030-drops-206395},
  doi =		{10.4230/LIPIcs.MFCS.2024.83},
  annote =	{Keywords: Derandomization, logspace computation, leakage-resilient hardness, psuedorandom generators}
}

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Leakage-Resilient Hardness Equivalence to Logspace Derandomization

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