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."
@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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