Nonuniform Kolmogorov extractors
Marius Zimand
TL;DR
This paper determines the precise amount of nonuniform advice needed to extract nearly perfect randomness from sources with suboptimal randomness rates, establishing tight bounds on advice complexity.
Contribution
It provides tight bounds on the nonuniform advice required for extracting high-quality randomness from sources with lower randomness rates.
Findings
O(1) advice is insufficient for extraction
Omega(1) advice is sufficient for extraction
Established tight bounds on advice complexity
Abstract
We establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a single source of randomness with lower randomness rate. More precisely, as instantiations of more general results, we show that while O(1) amount of advice regarding the source is not enough for extracting a string with randomness rate 1 from a source string with constant subunitary random rate, \omega(1) amount of advice is.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Complexity and Algorithms in Graphs · Cryptography and Data Security