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Abstract: For every binary sequence A, there is an infinite binary sequence S such that A P tt S and S is stochastic in the sense of Kolmogorov and Loveland. 1 Introduction In the mid-1960's, Martin-Lof [23] used the general theory of algorithms to formulate the first successful definition of the randomness of individual binary sequences. Subsequent definitions, using a variety of conceptual approaches, were introduced by Levin [17], Schnorr [24, 25], Chaitin [6, 7, 8], Solovay [28], and Shen 0... (Update)
Context of citations to this paper: More
...properly contained in the class of Kolmogorov Loveland stochastic sequences. The technique has also been employed by Lutz and Schweizer [8] in order to show that every sequence can be reduced to a Kolmogorov Loveland stochastic set via a truth table reduction computable in...
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BibTeX entry: (Update)
J. H. Lutz and D. L. Schweizer. Feasible reductions to Kolmogorov-Loveland stochastic sequences. Theoretical Computer Science, 225:185-194, 1999. http://citeseer.ist.psu.edu/lutz99feasible.html More
@article{ lutz99feasible,
author = "Jack H. Lutz and David L. Schweizer",
title = "Feasible reductions to {Kolmogorov--Loveland} stochastic sequences",
journal = "Theoretical Computer Science",
volume = "225",
number = "1--2",
pages = "185--194",
year = "1999",
url = "citeseer.ist.psu.edu/lutz99feasible.html" }
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110 A theory of program size formally identical to information t.. - Chaitin - 1975
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63 the definition of random sequences (context) - Martin-Lof - 1966
40 Process complexity and effective random tests (context) - Schnorr - 1973
33 A unified approach to the definition of random sequences (context) - Schnorr - 1971
29 Theoretical Computer Science (context) - Juedes, Lathrop et al. - 1994
27 Soviet Mathematics Doklady (context) - Levin, notion et al. - 1973
26 Logical depth and physical complexity (context) - Bennett - 1988
26 Bulletin of the American Mathematical Society (context) - Church, concept et al. - 1940
19 On tables of random numbers (context) - Kolmogorov - 1963
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13 Combinatorial foundations of information theory and calculus.. (context) - Kolmogorov - 1983
12 Incompleteness theorems for random reals - Chaitin - 1987
12 Grundlagen der Wahrscheinlichkeitsrechnung (context) - von Mises - 1919
10 A new interpretation of von Mises' concept of a random seque.. (context) - Loveland - 1966
9 translated in Theory of Probability and its Applications (context) - Kolmogorov, Uspenskii et al. - 1987
8 Department of Mathematics (context) - van Lambalgen, PhD - 1987
8 An observation on probability versus randomness with applica.. - Book, Lutz et al. - 1994
5 On languages reducible to algorithmically random languages (context) - Book - 1994
5 Equivalence of measures of complexity classes - Breutzmann, Lutz
5 Every sequence is reducible to a random one (context) - G'acs - 1986
4 On relations between different algorithmic definitions of ra.. (context) - Kh - 1989
3 The frequency approach to the definition of a random sequenc.. (context) - Kh - 1982
2 Die Widerspruchsfreiheit des Kollectivbegriffs in der Wahrsc.. (context) - Wald - 1938
1 The Kleene hierarchy classification of recursively random se.. (context) - Loveland - 1966
1 and complete extensions of PA (context) - Kucera, Pi - 1985
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