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DOI: 10.4230/LIPIcs.ITCS.2018.29
URN: urn:nbn:de:0030-drops-83300
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8330/
Hatami, Pooya ; Tal, Avishay
Pseudorandom Generators for Low Sensitivity Functions
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Abstract
A Boolean function is said to have maximal sensitivity s if s is the largest number of Hamming neighbors of a point which differ from it in function value. We initiate the study of pseudorandom generators fooling low-sensitivity functions as an intermediate step towards settling the sensitivity conjecture. We construct a pseudorandom generator with seed-length 2^{O(s^{1/2})} log(n) that fools Boolean functions on n variables with maximal sensitivity at most s. Prior to our work, the (implicitly) best pseudorandom generators for this class of functions required seed-length 2^{O(s)} log(n).
BibTeX - Entry
@InProceedings{hatami_et_al:LIPIcs:2018:8330,
author = {Pooya Hatami and Avishay Tal},
title = {{Pseudorandom Generators for Low Sensitivity Functions}},
booktitle = {9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
pages = {29:1--29:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-060-6},
ISSN = {1868-8969},
year = {2018},
volume = {94},
editor = {Anna R. Karlin},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8330},
URN = {urn:nbn:de:0030-drops-83300},
doi = {10.4230/LIPIcs.ITCS.2018.29},
annote = {Keywords: Pseudorandom Generators, Sensitivity, Sensitivity Conjecture}
}
| Keywords: | Pseudorandom Generators, Sensitivity, Sensitivity Conjecture | |
| Seminar: | 9th Innovations in Theoretical Computer Science Conference (ITCS 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 12.01.2018 |
