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CORR
2011
Springer

Symmetry of information and bounds on nonuniform randomness extraction via Kolmogorov extractors

8 years 7 days ago
Symmetry of information and bounds on nonuniform randomness extraction via Kolmogorov extractors
We prove a strong Symmetry of Information relation for random strings (in the sense of Kolmogorov complexity) and 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. More precisely, as instantiations of more general results, we show: • For all n-bit random strings x and y, x is random conditioned by y if and only if y is random conditioned by x; • 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 random rate, ω(1) amount of advice is. The proofs use Kolmogorov extractors as the main technical device.
Marius Zimand
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Marius Zimand
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