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Abstract: This paper is a survey of concepts and results related to simple Kolmogorov complexity, prefix complexity and resource-bounded complexity. We also consider a new type of complexity--- statistical complexity closely related to mathematical statistics. Unlike other discoverers of algorithmic complexity, A. N. Kolmogorov's leading motive was developing on its basis a mathematical theory more adequately substantiating applications of probability theory, mathematical statistics and information... (Update)
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.... studied before, for example as related to the Kolmogorov structure function [14, 2] and absolutely non stochastic objects [14, 17, 15, 18], notions also defined or suggested by Kolmogorov at the mentioned meeting. For the relation with inductive reasoning according to...
.... function) as a measure of stochasticity was introduced by Kolmogorov in the seventies [1] 4] 3] and studied by Levin and V yugin [9] [10]. Evidently, the snooping function is non negative and non decreasing. For any sequence x we have by (2) L x (ff c) l(x) for each...
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Complexity Approximation Principle - Vovk, Gammerman (1999) (Correct)
Does Snooping Help? - V'yugin (1999) (Correct)
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3: An Introduction to Kolmogorov Complexity and Its Applications - Li, Vitanyi - 1997
2: Aggregating strategies (context) - Vovk - 1990
2: the defect of randomness of a finite object with respect to measures with given .. (context) - V'yugin - 1987
BibTeX entry: (Update)
V.V. V'yugin, Algorithmic complexity and stochastic properties of finite binary sequences, The Computer Journal, 42:4(1999), 294--317. http://citeseer.ist.psu.edu/482199.html More
@misc{ v'yugin99algorithmic,
author = "V. V'yugin",
title = "Algorithmic complexity and stochastic properties of finite binary sequences",
text = "V.V. V'yugin, Algorithmic complexity and stochastic properties of finite
binary sequences, The Computer Journal, 42:4(1999), 294--317.",
year = "1999",
url = "citeseer.ist.psu.edu/482199.html" }
Citations (may not include all citations):660 An Introduction to Kolmogorov Complexity and Its Application.. - Li, Vitanyi - 1997
229 Theory of Recursive Functions and Effective Computability (context) - Rogers - 1967
216 A universal prior for integers and estimation by minimum des.. (context) - Rissanen - 1983
169 A formal theory of inductive inference (context) - Solomonoff - 1964
159 Three approaches to the quantitative definition of informati.. (context) - Kolmogorov - 1965
132 Estimation and inference by compact coding (context) - Wallace, Freeman - 1987
110 A theory of program size formally identical to information t.. - Chaitin - 1975
99 Algorithmic information theory - Chaitin - 1977
99 Algorithmic Information Theory - Chaitin - 1987
66 Theory of Statistics (context) - Schervish - 1995
62 Minimum description length principle (context) - Rissanen - 1985
45 the symmetry of algorithmic information (context) - Gacs - 1974
36 The logical basis for information theory and probability the.. (context) - Kolmogorov - 1968
31 Complexity-based induction systems: Comparisons and converge.. (context) - Solomonoff - 1978
23 the notion of random sequence (context) - Levin - 1973
19 On tables of random numbers (context) - Kolmogorov - 1963
18 Universal search problems (context) - Levin - 1973
13 Relations between varieties of Kolmogorov complexities (context) - Uspensky, Shen - 1996
12 Kolmogorov's contributions to information theory and algorit.. (context) - Cover, Gacs et al. - 1989
11 Some equivalences between Shannon entropy and Kolmogorov com.. (context) - Leung-Yan-Chrong, Cover - 1978
11 Randomness conservation inequalities; information and indepe.. (context) - Levin - 1984
9 the defect of randomness of a finite object with respect to .. (context) - V'yugin - 1987
8 The complexity of finite objects and the algorithmic concept.. (context) - Zvonkin, Levin - 1970
8 Can an individual sequence of zeros and ones be random (context) - Uspensky, Semenov et al. - 1990
8 Common information is far less than mutual information (context) - Gacs, Korner - 1973
8 Prequential probability: principles and properties - Dawid, Vovk - 1997
7 Various measures of complexity for finite objects (context) - Levin - 1976
7 Minimum description length estimators under the optimal codi.. (context) - Vovk - 1995
6 the length of programs for computing binary sequences (context) - Chaitin - 1966
6 Algorithms and randomness (context) - Kolmogorov, Uspensky - 1987
5 Statistical properties of finite sequences with high Kolmogo.. - Li, Vitanyi - 1994
5 Random Sequences (context) - Lambalgen - 1987
4 the concept of the Bernoulli property (context) - Vovk - 1986
4 Learning about parameter of the Bernoulli model (context) - Vovk - 1997
3 stochasticity in the Kolmogorov sense and its properties (context) - Shen, concept - 1983
3 On common information (context) - Muchnik - 1998
2 Laws of information conservation (context) - Levin - 1974
2 Combinatorial basis of information theory and probability th.. (context) - Kolmogorov - 1983
1 Kolmogorovskaya slozhnost' dvadsat' let spustia (context) - Li, Vitanyi - 1988
1 The logic in computer science column - Gurevich - 1988
1 Some properties of Kolmogorov # random finite sequences (context) - Asarin - 1987
1 A logic of probability (context) - Vovk - 1993
1 the length of programs for computing binary sequences: stati.. (context) - Chaitin - 1969
1 and Semenov (context) - Uspensky
1 and Uspensky (context) - Kolmogorov
Documents on the same site (http://www3.oup.co.uk/computer_journal/hdb/Volume_42/Issue_04/): More
Rejoinder - Wallace, Dowe (1999) (Correct)
Hypothesis Selection and Testing by the MDL Principle - Rissanen (1998) (Correct)
Discussion of the Papers by Rissanen and by Wallace and Dowe - Dawid (Correct)
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