Prediction from partial information and hindsight, an alternative proof

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00489470" target="_blank" >RIV/67985840:_____/18:00489470 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ipl.2018.04.011" target="_blank" >http://dx.doi.org/10.1016/j.ipl.2018.04.011</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ipl.2018.04.011" target="_blank" >10.1016/j.ipl.2018.04.011</a>

Result language
angličtina
Original language name
Prediction from partial information and hindsight, an alternative proof
Original language description
Let X be a random variable distributed over n-bit strings with H(X)≥n−k, where k«n. Using subadditivity we know that the average coordinate has high entropy. Meir and Wigderson [1] showed that a random coordinate looks random to an adversary who is allowed to query around n/k other coordinates non-deterministically. They used this result to obtain top-down arguments in depth-3 circuit lower bounds. In this note we give an alternative proof of their main result which tightens their parameters. Our proof is inspired by a paper of Paturi, Pudlák and Zane [3] who gave a non-trivial k-SAT algorithm and tight depth-3 circuit lower bounds for parity.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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