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Feasible reductions to kolmogorov-loveland stochastic sequences

1999
*
Theoretical Computer Science
*

For every binary sequence A, there is an infinite binary sequence S such that A <ft S

doi:10.1016/s0304-3975(99)00041-9
fatcat:c4vufjke5nfehg75paujnnlgli
*and*S is*stochastic*in the sense of*Kolmogorov**and**Loveland*. ... Acknowledgement The second author gratefUlly acknowledges the hospitality of Dan Ashlock*and*the Iowa State University Department of Mathematics, where he was a visitor when this research was conducted ... The main theorem also implies that the class RAND of all random oracles cannot be replaced by the class KL-STOCH of all*Kolmogorov*-*Loveland**stochastic*oracles in some known characterizations of*complexity*...##
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An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory

2008
*
Entropy
*

Instead of static entropy we assert that the

doi:10.3390/entropy-e10010006
fatcat:c2zsot7amjhobfoqae5ombhg4e
*Kolmogorov**complexity*of a static structure such as a solid is the proper measure of disorder (or chaoticity). ... Through the inequality that relates*stochasticity**and*chaoticity of random binary sequences we maintain that Lin's notion of stability corresponds to the stability of the frequency of 1s in the selected ... When subsequences selected by such a selection rule pass the unbiasness test they are called*Kolmogorov*-*Loveland**stochastic*(KL-*stochastic*for short). ...##
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The complexity of stochastic sequences

2008
*
Journal of computer and system sciences (Print)
*

We review

doi:10.1016/j.jcss.2007.06.018
fatcat:mx3t5w5s25ejvduduooqg72574
*and*slightly strengthen known results on the*Kolmogorov**complexity*of prefixes of effectively random sequences. ... Furthermore, we demonstrate that there is no Mises-Wald-Church*stochastic*sequence such that all non-empty prefixes of the sequence have*Kolmogorov**complexity*O(log n). ... Acknowledgments We thank Klaus Ambos-Spies, Nicolai Vereshchagin,*and*Paul Vitányi for helpful discussions*and*Jack Lutz, Alexander Shen,*and*the anonymous referees for their comments. ...##
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Kolmogorov and mathematical logic

1992
*
Journal of Symbolic Logic (JSL)
*

In my life, in my personal experience, there were three such men,

doi:10.2307/2275276
fatcat:j5x5hcf4nrfz7jsk62mx2sp264
*and*one of them was Andrei Nikolaevich*Kolmogorov*. I was lucky enough to be his immediate pupil. ...*Kolmogorov*was not only one of the greatest mathematicians of the twentieth century. By the width of his scientific interests*and*results he reminds one of the titans of the Renaissance. ... So the sequences that are random in von Mises', Church's*and*Kolmogorov's sense should be called respectively "*stochastic*", "Church*stochastic*"*and*"*Kolmogorov**stochastic*". ...##
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Randomness
[article]

2001
*
arXiv
*
pre-print

to

arXiv:math/0110086v2
fatcat:jqstqwkyvrgh3onpviqq3k4iny
*Kolmogorov**Complexity**and*Its Applications" (M. ... Li*and*P. Vitanyi), 2nd Ed., Springer-Verlag, 1997. ...*Kolmogorov**and*V.A. Uspensky, SIAM J. Theory Probab. Appl., 32(1987), 387-412]. N.*Kolmogorov*[Sankhyā, Ser. A, 25(1963), 369-376]*and*Donald William*Loveland*(1934-) [Z. Math. Logik Grundl. ...##
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Page 5099 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

All infinite sequences R random in the sense of Martin-Lof have a property called

*Kolmogorov*-*Loveland*(K-L)*stochasticity*: if a subsequence A of R is chosen according to a (very broadly defined) “admissible ... Feasible reductions to Kolmogoroy-*Loveland**stochastic*sequences. (English summary) Theoret. Comput. Sci. 225 (1999), no. 1-2, 185-194. ...##
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Page 2001 of Mathematical Reviews Vol. 58, Issue 3
[page]

1979
*
Mathematical Reviews
*

*Kolmogorov*, D.

*Loveland*, P. Martin-Lof

*and*R. J. ... Fine, Terrence L. 58 #13240 A computational

*complexity*viewpoint on the stability of relative frequency

*and*on

*stochastic*independence. ...

##
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Algorithms and Randomness

1988
*
Theory of Probability and its Applications
*

The review articles [30]

doi:10.1137/1132060
fatcat:ttnurlwgerfrpgpbssi5ghiu7q
*and*[31] refer to Church*stochastic*sequences as "Mises-Church random sequences"*and*to*Kolmogorov**stochastic*sequences as "Mises-*Kolmogorov*-*Loveland*random sequences." ... It is not even known whether any subsequence formed by applying a*Kolmogorov*admissible rule to a*Kolmogorov**stochastic*sequence is itself a*Kolmogorov**stochastic*. ...##
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Mathematical Foundations of Randomness
[chapter]

2011
*
Philosophy of Statistics
*

Bandyopadhyay

doi:10.1016/b978-0-444-51862-0.50021-6
fatcat:7pik7bt4hzcureaxtkt4mjcdia
*and*the anonymous referee for several useful suggestions. ... Thus*Kolmogorov*-*Loveland*randomness is strictly stronger than*Kolmogorov*-*Loveland**stochasticity*, partial computable randomness is strictly stronger than Mises-Wald-Church*stochasticity*,*and*computable ...*Kolmogorov*-*Loveland*Partial Computably Computably Random (KLR) Random (PCR) Random (CR) Place selection*Kolmogorov*-*Loveland*Mises-Wald-Church Church*Stochastic*(KLS)*Stochastic*(MWCS)*Stochastic*...##
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Book Review: Kolmogorov complexity and algorithmic randomness

2019
*
Bulletin of the American Mathematical Society
*

Acknowledgments I am indebted to Manuel Blum, Qi Cheng, Eviatar Procaccia, Salil Vadhan,

doi:10.1090/bull/1676
fatcat:qrtd3szbrnfvrgdwuzz5lszxua
*and*David Zuckerman for their patience with,*and*answers to, my many naive questions. ...*Kolmogorov**complexity*. ... The account of*Kolmogorov**complexity**and*randomness in [SUV] is masterful. ...##
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Kolmogorov–Loveland randomness and stochasticity

2006
*
Annals of Pure and Applied Logic
*

The concept is named after

doi:10.1016/j.apal.2005.06.011
fatcat:4de2qsox65eb5cx2svnguy2wxy
*Kolmogorov*(9)*and**Loveland*(14) , who studied non-monotonic selection rules to define accordant*stochasticity*concepts, which we will describe later. ... nondecreasing,*and*unbounded function g*and*almost all n, the prefix of A of length n has prefix-free*Kolmogorov**complexity*at least n − g(n). ... Acknowledgments We are grateful to Klaus Ambos-Spies, Rod Downey, Antonín Kučera, Stephen Lempp, Jack Lutz, Boris Ryabko,*and*Ted Slaman for helpful discussion. Bibliography ...##
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Kolmogorov-Loveland Randomness and Stochasticity
[chapter]

2005
*
Lecture Notes in Computer Science
*

nondecreasing,

doi:10.1007/978-3-540-31856-9_35
fatcat:xhqu5agth5ewxd7wps34pzcmfq
*and*unbounded function g*and*almost all n, the prefix of A Introduction of length n has prefix-free*Kolmogorov**complexity*of at least n − g(n). ... by a factor of α < 1 with respect to prefix-free*Kolmogorov**complexity*. ... Acknowledgments We are grateful to Klaus Ambos-Spies, Rod Downey, Antonín Kučera, Stephen Lempp, Jack Lutz, Boris Ryabko,*and*Ted Slaman for helpful discussion. ...##
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Andrei Nikolaevich Kolmogorov, 25 April 1903 - 20 October 1987

1991
*
Biographical Memoirs of Fellows of the Royal Society
*

It was in the

doi:10.1098/rsbm.1991.0015
fatcat:7t3rg7l2cre3pdyinufdyoiahu
*Kolmogorov*home at Tunoshna that ANK spent his earliest years. ... Andrei Nikolaevich is always known to us by the family name of his maternal grandfather Yakov Stepanovich*Kolmogorov*, a leading member of the Uglich nobility. ... The portrait photograph shows*Kolmogorov*lecturing his Moscow schoolchildren. R e f e r e n c e s ...##
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The dimensions of individual strings and sequences

2003
*
Information and Computation
*

The

doi:10.1016/s0890-5401(03)00187-1
fatcat:na6axs36qzchdo2eojhtgkr7t4
*Kolmogorov**complexity*of a string is proven to be the product of its length*and*its dimension. ... This gives a new characterization of algorithmic information*and*a new proof of Mayordomo's recent theorem stating that the dimension of a sequence is the limit inferior of the average*Kolmogorov**complexity*... of his*and*Ryabko's earlier work on Hausdorff dimension,*Kolmogorov**complexity*,*and*martingales. ...##
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Random scattering of bits by prediction
[article]

2010
*
arXiv
*
pre-print

Bad learners generate mistake sequences that are atypically

arXiv:0909.3648v2
fatcat:m6sckhxd5ngidoftu2qxfp2dq4
*complex*or diverge*stochastically*from a purely random Bernoulli sequence. ... We obtain estimates of their error, algorithmic*complexity**and*divergence from a purely random Bernoulli sequence. ... When subsequences selected by such a selection rule pass the unbiasedness test they are called*Kolmogorov*-*Loveland**stochastic*(KL-*stochastic*for short). ...
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