The intractability of computing the Hamming distance
نویسندگان
چکیده
منابع مشابه
The Intractability of Computing the Hamming Distance
Given a string x and a language L, the Hamming distance of x to L is the minimum Hamming distance of x to any string in L. The edit distance of a string to a language is analogously defined. First, we prove that there is a language in AC such that both Hamming and edit distance to this language are hard to approximate; they cannot be approximated with factor O(n 1 3 − ), for any > 0, unless P =...
متن کاملOn Computing the Hamming Distance
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.
متن کاملThe Intractability of Computingthe Hamming
Given a language L, the Hamming distance of a string x to L is the minimum Hamming distance of x to any string in L. The edit distance of a string to a given language is deened similarly. First, we prove that the Hamming distance to languages in AC 0 is hard to approximate; it cannot be approximated within a factor O ? n 1 3 ? , for any > 0, unless P = NP (n denotes the length of the input stri...
متن کاملThe intractability of computing the minimum distance of a code
It is shown that the problem of computing the minimum distance of a binary linear code is NP-hard, and the corresponding decision problem is NP-complete. This result constitutes a proof of the conjecture of Berlekamp, McEliece, and van Tilborg, dating back to 1978. Extensions and applications of this result to other problems in coding theory are discussed.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2005
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2005.02.002