An Excursion to the Kolmogorov Random Strings
نویسندگان
چکیده
منابع مشابه
An Excursion to the Kolmogorov Random Strings
We study the set of resource bounded Kolmogorov random strings: R t = fx j K t (x) jxjg for t a time constructible function such that t(n) 2 n 2 and t(n) 2 2 n O(1). We show that the class of sets that Tur-ing reduce to R t has measure 0 in EXP with respect to the resource-bounded measure introduced by 17]. From this we conclude that R t is not Turing-complete for EXP. This contrasts the resour...
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We show the following results for polynomial-time reducibility to RC, the set of Kolmogorov random strings. 1. If P 6= NP, then SAT does not dtt-reduce to RC. 2. If PH does not collapse, then SAT does not n--reduce to RC for any α < 1. 3. If PH does not collapse, then SAT does not n-T-reduce to RC for any α < 2 . 4. There is a problem in E that does not dtt-reduce to RC. 5. There is a problem i...
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We investigate the question of whether one can characterize complexity classes (such as PSPACE or NEXP) in terms of efficient reducibility to the set of Kolmogorovrandom strings RC. We show that this question cannot be posed without explicitly dealing with issues raised by the choice of universal machine in the definition of Kolmogorov complexity. Among other results, we show that although for ...
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The Kolmogorov complexity of a string is the length of the shortest program that generates it. A binary string is said to have trivial Kolmogorov complexity if its complexity is at most the complexity of its length. Intuitively, such strings carry no more information than the information that is inevitably coded into their length (which is the same as the information coded into a sequence of 0s...
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We study reals with infinitely many incompressible prefixes. Call A ∈ 2 Kolmogorov random if (∃∞n) C(A n) > n − O(1), where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by Martin-Löf, Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random.1 Together with the converse—proved by Nies, Stephan and Terwijn [11]—this provides a natural c...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1997
ISSN: 0022-0000
DOI: 10.1006/jcss.1997.1484