Journal of Symbolic Logic 68 (4):1362-1376 (2003)
Abstract |
It is shown that the class of Kolmogorov-Loveland stochastic sequences is not closed under selecting subsequences by monotonic computable selection rules. This result gives a strong negative answer to the question whether the Kolmogorov-Loveland stochastic sequences are closed under selecting sequences by Kolmogorov-Loveland selection rules, i.e., by not necessarily monotonic, partial computable selection rules. The following previously known results are obtained as corollaries. The Mises-Wald-Church stochastic sequences are not closed under computable permutations, hence in particular they form a strict superclass of the class of Kolmogorov-Loveland stochastic sequences. The Kolmogorov-Loveland selection rules are not closed under composition
|
Keywords | No keywords specified (fix it) |
Categories | (categorize this paper) |
DOI | 10.2178/jsl/1067620192 |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
A New Interpretation of the von Mises' Concept of Random Sequence.Donald Loveland - 1966 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 12 (1):279-294.
Citations of this work BETA
Kolmogorov–Loveland Randomness and Stochasticity.Wolfgang Merkle, Joseph S. Miller, André Nies, Jan Reimann & Frank Stephan - 2006 - Annals of Pure and Applied Logic 138 (1):183-210.
Constructive Equivalence Relations on Computable Probability Measures.Laurent Bienvenu & Wolfgang Merkle - 2009 - Annals of Pure and Applied Logic 160 (3):238-254.
Uniform Distribution and Algorithmic Randomness.Jeremy Avigad - 2013 - Journal of Symbolic Logic 78 (1):334-344.
Computable Randomness and Betting for Computable Probability Spaces.Jason Rute - 2016 - Mathematical Logic Quarterly 62 (4-5):335-366.
How Much Randomness is Needed for Statistics?Bjørn Kjos-Hanssen, Antoine Taveneaux & Neil Thapen - 2012 - In S. Barry Cooper (ed.), Annals of Pure and Applied Logic. pp. 395--404.
View all 7 citations / Add more citations
Similar books and articles
General Random Sequences and Learnable Sequences.C. P. Schnorr & P. Fuchs - 1977 - Journal of Symbolic Logic 42 (3):329-340.
Relative Lawlessness in Intuitionistic Analysis.Joan Rand Moschovakis - 1987 - Journal of Symbolic Logic 52 (1):68-88.
Kolmogorov Complexity and Information Theory. With an Interpretation in Terms of Questions and Answers.Peter D. Grünwald & Paul M. B. Vitányi - 2003 - Journal of Logic, Language and Information 12 (4):497-529.
Laver Sequences for Extendible and Super-Almost-Huge Cardinals.Paul Corazza - 1999 - Journal of Symbolic Logic 64 (3):963-983.
Enumerations of the Kolmogorov Function.Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan & Leen Torenvliet - 2006 - Journal of Symbolic Logic 71 (2):501 - 528.
Kolmogorov Complexity for Possibly Infinite Computations.Verónica Becher & Santiago Figueira - 2005 - Journal of Logic, Language and Information 14 (2):133-148.
Every 2-Random Real is Kolmogorov Random.Joseph S. Miller - 2004 - Journal of Symbolic Logic 69 (3):907-913.
Analytics
Added to PP index
2009-01-28
Total views
21 ( #537,621 of 2,520,899 )
Recent downloads (6 months)
1 ( #405,457 of 2,520,899 )
2009-01-28
Total views
21 ( #537,621 of 2,520,899 )
Recent downloads (6 months)
1 ( #405,457 of 2,520,899 )
How can I increase my downloads?
Downloads