Randomness extraction and asymptotic Hamming distance
نویسندگان
چکیده
منابع مشابه
Randomness extraction and asymptotic Hamming distance
We obtain a non-implication result in the Medvedev degrees by studying sequences that are close to Martin-Löf 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.
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Let x, y be strings of equal length. The Hamming distance h(x, y) between x and y is the number of positions in which x and y differ. If x is a cyclic shift of y, we say x and y are conjugates. We consider f(x, y), the Hamming distance between the conjugates xy and yx. Over a binary alphabet f(x, y) is always even, and must satisfy a further technical condition. By contrast, over an alphabet of...
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Methods for the fast computation of Hamming distance developed for the case of large number of pairs of words are presented and discussed in the paper. The connection of this subject to some questions about intersecting sets and Hadamard designs is also considered.
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2013
ISSN: 1860-5974
DOI: 10.2168/lmcs-9(3:27)2013