All reports by Author Maria Lopez-Valdes:

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TR06-077
| 12th June 2006
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Maria Lopez-Valdes#### Lempel-Ziv Dimension for Lempel-Ziv Compression

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TR06-047
| 11th February 2006
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Maria Lopez-Valdes#### Scaled Dimension of Individual Strings

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TR04-104
| 19th November 2004
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Maria Lopez-Valdes, Mayordomo Elvira#### Dimension is compression

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TR04-029
| 7th April 2004
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John Hitchcock, Maria Lopez-Valdes, Elvira Mayordomo#### Scaled dimension and the Kolmogorov complexity of Turing hard sets

Maria Lopez-Valdes

This paper describes the Lempel-Ziv dimension (Hausdorff like

dimension inspired in the LZ78 parsing), its fundamental properties

and relation with Hausdorff dimension.

It is shown that in the case of individual infinite sequences, the

Lempel-Ziv dimension matches with the asymptotical Lempel-Ziv

compression ratio.

This fact is used to describe results ... more >>>

Maria Lopez-Valdes

We define a new discrete version of scaled dimension and we find

connections between the scaled dimension of a string and its Kolmogorov

complexity and predictability. We give a new characterization

of constructive scaled dimension by Kolmogorov complexity, and prove

a new result about scaled dimension and prediction.

Maria Lopez-Valdes, Mayordomo Elvira

Effective fractal dimension was defined by Lutz (2003) in order to quantitatively analyze the structure of complexity classes.

Interesting connections of effective dimension with information theory were also found, in fact the cases of polynomial-space and constructive dimension can be precisely characterized in terms of Kolmogorov complexity, while analogous ...
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John Hitchcock, Maria Lopez-Valdes, Elvira Mayordomo

Scaled dimension has been introduced by Hitchcock et al (2003) in order to quantitatively distinguish among classes such as SIZE(2^{a n}) and SIZE(2^{n^{a}}) that have trivial dimension and measure in ESPACE.

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