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Derandomizing from Random Strings
"... In this paper we show that BPP is truthtable reducible to the set of Kolmogorov random strings RK. It was previously known that PSPACE, and hence BPP is Turingreducible to RK. The earlier proof relied on the adaptivity of the Turingreduction to find a Kolmogorovrandom string of polynomial length ..."
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Cited by 9 (2 self)
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In this paper we show that BPP is truthtable reducible to the set of Kolmogorov random strings RK. It was previously known that PSPACE, and hence BPP is Turingreducible to RK. The earlier proof relied on the adaptivity of the Turingreduction to find a Kolmogorovrandom string of polynomial length
On the computational power of random strings
 Annals of Pure and Applied Logic
"... Abstract. There are two fundamental computably enumerable sets associated with any Kolmogorov complexity measure. These are the set of nonrandom strings and the overgraph. This paper investigates the computational power of these sets. It follows work done by Kummer, Muchnik and Positselsky, and All ..."
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Cited by 3 (1 self)
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Abstract. There are two fundamental computably enumerable sets associated with any Kolmogorov complexity measure. These are the set of nonrandom strings and the overgraph. This paper investigates the computational power of these sets. It follows work done by Kummer, Muchnik and Positselsky
On generating independent random strings
"... It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two initial strings are random, then the above task can be performed ..."
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Cited by 3 (2 self)
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It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two initial strings are random, then the above task can
On generating independent random strings
"... It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two initial strings are random, then the above task can be performed ..."
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It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two initial strings are random, then the above task can
What Is a Random String?
, 1995
"... Chaitin's algorithmic definition of random strings  based on the complexity induced by selfdelimiting computers  is critically discussed. One shows that Chaitin's model satisfy many natural requirements related to randomness, so it can be considered as an adequate model for nite rando ..."
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Cited by 1 (0 self)
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Chaitin's algorithmic definition of random strings  based on the complexity induced by selfdelimiting computers  is critically discussed. One shows that Chaitin's model satisfy many natural requirements related to randomness, so it can be considered as an adequate model for nite
An Excursion to the Kolmogorov Random Strings
 In Proceedings of the 10th IEEE Structure in Complexity Theory Conference
, 1995
"... 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 Turing reduce to R t has measure 0 in EXP with respect to the resourcebounded measure ..."
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Cited by 20 (10 self)
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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 Turing reduce to R t has measure 0 in EXP with respect to the resourcebounded measure
Power from Random Strings
 IN PROCEEDINGS OF THE 43RD IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2002
"... We show that sets consisting of strings of high Kolmogorov complexity provide examples of sets that are complete for several complexity classes under probabilistic and nonuniform reductions. These sets are provably not complete under the usual manyone reductions. Let ..."
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Cited by 41 (17 self)
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We show that sets consisting of strings of high Kolmogorov complexity provide examples of sets that are complete for several complexity classes under probabilistic and nonuniform reductions. These sets are provably not complete under the usual manyone reductions. Let
Hitting properties of a random string
 ELECTRONIC J. PROBAB
, 2002
"... We consider Funaki’s model of a random string taking values in R d. It is specified by the following stochastic PDE, ∂u(x) ∂t = ∂2 u(x) ..."
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Cited by 15 (6 self)
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We consider Funaki’s model of a random string taking values in R d. It is specified by the following stochastic PDE, ∂u(x) ∂t = ∂2 u(x)
On the complexity of random strings (Extended Abstract)
 IN STACS 96
, 1996
"... We show that the set R of Kolmogorov random strings is truthtable complete. This improves the previously known Turing completeness of R and shows how the halting problem can be encoded into the distribution of random strings rather than using the time complexity of nonrandom strings. As an applic ..."
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Cited by 14 (1 self)
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We show that the set R of Kolmogorov random strings is truthtable complete. This improves the previously known Turing completeness of R and shows how the halting problem can be encoded into the distribution of random strings rather than using the time complexity of nonrandom strings
Rare Events in Random Strings
"... Some stringsthe texts are assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or underrepresentation of a word or a set of words. The aim of this paper is twofold. ..."
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Cited by 1 (1 self)
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Some stringsthe texts are assumed to be randomly generated, according to a probability model that is either a Bernoulli model or a Markov model. A rare event is the over or underrepresentation of a word or a set of words. The aim of this paper is twofold.
Results 1  10
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