Randomness extraction and asymptotic Hamming distance

Abstract

We obtain a non-implication result in the Medvedev degrees by studying sequences that are close to Martin-L\"of random in asymptotic Hamming distance. Our result is that the class of stochastically bi-immune sets is not Medvedev reducible to the class of sets having complex packing dimension 1.

Keywords

• mathematics - logic
• computer science - computational complexity
• computer science - information theory
• computer science - logic in computer science