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Abstract: Classical Hausdor dimension (sometimes called fractal dimension) was recently e ectivized using gales (betting strategies that generalize martingales), thereby endowing various complexity classes with dimension structure and also de ning the constructive dimensions of individual binary (in nite) sequences. In this paper we use gales computed by multi-account nite-state gamblers to develop the nite-state dimensions of sets of binary sequences and individual binary sequences. The theorem of... (Update)
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...the nite state version of our k = 2 graph in Figure 1. This equivalence follows from the recent proof by Dai, Lathrop, Lutz, and Mayordomo [5] of the equivalence of nite state dimension and nite state compressibility. 2 Preliminaries We work in an arbitrary nite alphabet...
...dimensions. Subsequently, Dai, Lathrop, Lutz, and Mayordomo used gales induced by nite state gamblers to de ne nite state dimension [2]. Fortnow and Lutz [4] also de ned feasible, computable, and nite state predictability. All the results mentioned in this introduction also...
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3: Fractal Geometry: Mathematical Foundations and Applications (context) - Falconer - 1990
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BibTeX entry: (Update)
J. J. Dai, J. I. Lathrop, J. H. Lutz, and E. Mayordomo. Finite-state dimension. In Proceedings of the Twenty-Eighth International Colloquium on Automata, Languages, and Programming, pages 1028-1039. Springer-Verlag, 2001. http://citeseer.ist.psu.edu/dai01finitestate.html More
@article{ dai01finitestate,
author = "Jack J. Dai and James I. Lathrop and Jack H. Lutz and Elvira Mayordomo",
title = "Finite-State Dimension",
journal = "Lecture Notes in Computer Science",
volume = "2076",
pages = "1028--??",
year = "2001",
url = "citeseer.ist.psu.edu/dai01finitestate.html" }
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