The Intractability of Computingthe Hamming
نویسنده
چکیده
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 string). Second, we show the parameterised intractability of computing the Ham-ming distance. We prove that for every t 2 N there exists a language in AC 0 such that the problem of computing the Hamming distance is W t-hard. Moreover , there is a language in P such that computing the Hamming distance to it is W P-hard. Furthermore, we show that the problems of computing the Hamming distance and of computing the edit distance are in some sense equivalent by presenting reductions from the former to the latter problem and vice versa.
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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 =...
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