Lempel-ziv dimension for lempel-ziv compression

Authors:
Maria Lopez-Valdes
Affiliations:
Departamento de Informática e Ing. de Sistemas, Universidad de Zaragoza, Zaragoza, Spain
Venue:
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Year:
2006

Citing 7
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Abstract

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 on Lempel-Ziv compression in terms of dimension of complexity classes and vice versa.