منابع مشابه
Gales Suffice for Constructive Dimension
Supergales, generalizations of supermartingales, have been used by Lutz (2002) to define the constructive dimensions of individual binary sequences. Here it is shown that gales, the corresponding generalizations of martingales, can be equivalently used to define constructive dimension.
متن کاملGales and supergales are equivalent for defining constructive Hausdorff dimension
We show that for a wide range of probability measures, constructive gales are interchangable with constructive supergales for defining constructive Hausdorff dimension, thus generalizing a previous independent result of Hitchcock [2] and partially answering an open question of Lutz [5].
متن کاملConstructive Dimension and Hausdorff Dimension: The Case of Exact Dimension
The present paper generalises results by Lutz and Ryabko. We prove a martingale characterisation of exact Hausdorff dimension. On this base we introduce the notion of exact constructive dimension of (sets of) infinite strings. Furthermore, we generalise Ryabko’s result on the Hausdorff dimension of the set of strings having asymptotic Kolmogorov complexity ≤ α to the case of exact dimension. Th...
متن کاملA Correspondence Principle for Exact Constructive Dimension
Exact constructive dimension as a generalisation of Lutz’s [Lut00, Lut03] approach to constructive dimension was recently introduced in [Sta11]. It was shown that it is in the same way closely related to a priori complexity, a variant of Kolmogorov complexity, of infinite sequences as their constructive dimension is related to asymptotic Kolmogorov complexity. The aim of the present paper is to...
متن کاملA Characterization of Constructive Dimension
In the context of Kolmogorov’s algorithmic approach to the foundations of probability, Martin-Löf defined the concept of an individual random sequence using the concept of a constructive measure 1 set. Alternate characterizations use constructive martingales and measures of impossibility. We prove a direct conversion of a constructive martingale into a measure of impossibility and vice versa, s...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2003
ISSN: 0020-0190
DOI: 10.1016/s0020-0190(02)00454-4