Santha-Vazirani sources, deterministic condensers and very strong extractors
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00531290" target="_blank" >RIV/67985840:_____/20:00531290 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1007/s00224-020-09975-8" target="_blank" >https://doi.org/10.1007/s00224-020-09975-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00224-020-09975-8" target="_blank" >10.1007/s00224-020-09975-8</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Santha-Vazirani sources, deterministic condensers and very strong extractors
Popis výsledku v původním jazyce
The notion of semi-random sources, also known as Santha-Vazirani (SV) sources, stands for a sequence of n bits, where the dependence of the i’th bit on the previousi − 1 bits is limited for every i ∈ [n]. If the dependence of the i’th bit on the remainingn − 1 bits is limited, then this is a strongSV-source. Even the strong SV -sources are known not to admit (universal) deterministic extractors, but they have seeded extractors, as their min-entropy is Ω n. It is intuitively obvious that strong SV -sources are more than just high-min-entropy sources, and this work explores the intuition. Deterministic condensers are known not to exist for general high-min-entropy sources, and we construct for any constants ε, δ ∈ (0,1) a deterministic condenser that maps n bits coming from a strong SV -source with bias at most δ to Ω n bits of min-entropy rate at least 1 − ε. In conclusion we observe that deterministic condensers are closely related to very strong extractors – a proposed strengthening of the notion of strong (seeded) extractors: in particular, our constructions can be viewed as very strong extractors for the family of strong Santha-Vazirani distributions. The notion of very strong extractors requires that the output remains unpredictable even to someone who knows not only the seed value (as in the case of strong extractors), but also the extractor’s outputs corresponding to the same input value with each of the preceding seed values (say, under the lexicographic ordering). Very strong extractors closely resemble the original notion of SV -sources, except that the bits must satisfy the unpredictability requirement only on average.
Název v anglickém jazyce
Santha-Vazirani sources, deterministic condensers and very strong extractors
Popis výsledku anglicky
The notion of semi-random sources, also known as Santha-Vazirani (SV) sources, stands for a sequence of n bits, where the dependence of the i’th bit on the previousi − 1 bits is limited for every i ∈ [n]. If the dependence of the i’th bit on the remainingn − 1 bits is limited, then this is a strongSV-source. Even the strong SV -sources are known not to admit (universal) deterministic extractors, but they have seeded extractors, as their min-entropy is Ω n. It is intuitively obvious that strong SV -sources are more than just high-min-entropy sources, and this work explores the intuition. Deterministic condensers are known not to exist for general high-min-entropy sources, and we construct for any constants ε, δ ∈ (0,1) a deterministic condenser that maps n bits coming from a strong SV -source with bias at most δ to Ω n bits of min-entropy rate at least 1 − ε. In conclusion we observe that deterministic condensers are closely related to very strong extractors – a proposed strengthening of the notion of strong (seeded) extractors: in particular, our constructions can be viewed as very strong extractors for the family of strong Santha-Vazirani distributions. The notion of very strong extractors requires that the output remains unpredictable even to someone who knows not only the seed value (as in the case of strong extractors), but also the extractor’s outputs corresponding to the same input value with each of the preceding seed values (say, under the lexicographic ordering). Very strong extractors closely resemble the original notion of SV -sources, except that the bits must satisfy the unpredictability requirement only on average.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
<a href="/cs/project/GX19-27871X" target="_blank" >GX19-27871X: Efektivní aproximační algoritmy a obvodová složitost</a><br>
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Theory of Computing Systems
ISSN
1432-4350
e-ISSN
—
Svazek periodika
64
Číslo periodika v rámci svazku
6
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
15
Strana od-do
1140-1154
Kód UT WoS článku
000528283000001
EID výsledku v databázi Scopus
2-s2.0-85084149923