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Abstract: Scaled dimension has been introduced by Hitchcock et al (2003) in order to quantitatively distinguish among classes such as SIZE(2 and SIZE(2 ) that have trivial dimension and measure in ESPACE. This paper gives an exact characterization of e#ective scaled dimension in terms of resource-bounded Kolmogorov complexity. We can now view each result on the scaled dimension of a class of languages as upper and lower bounds on the Kolmogorov complexity of the languages in the class. We prove a... (Update)
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BibTeX entry: (Update)
@misc{ hitchcock-scaled,
author = "John M. Hitchcock and Mara Lopez-Valdes and Elvira Mayordomo",
title = "Scaled dimension and the Kolmogorov complexity of Turing hard sets",
url = "citeseer.ist.psu.edu/703174.html" }
Citations (may not include all citations):660 An Introduction to Kolmogorov Complexity and its Application.. - Li, Vitanyi - 1997
142 Almost everywhere high nonuniform complexity - Lutz - 1992
128 A complexity-theoretic approach to randomness (context) - Sipser - 1983
49 Generalized Kolmogorov complexity and the structure of feasi.. (context) - Hartmanis - 1983
43 Randomness conservation inequalities; information and indepe.. (context) - Levin - 1984
42 The complexity and distribution of hard problems - Juedes, Lutz - 1995
31 Dimension in complexity classes - Lutz - 2003
15 dimension in exponential time (context) - Ambos-Spies, Merkle et al. - 2001
11 Theoretical Computer Science (context) - Ambos-Spies, Neis et al. - 1996
11 of Information (context) - Kolmogorov, to et al. - 1965
9 Resource-bounded Kolmogorov complexity of hard languages (context) - Huynh - 1986
9 Completeness and weak completeness under polynomial-size cir.. - Juedes, Lutz - 1996
9 a Link Between Computational Complexity and Information Theo.. (context) - Longpre, Kolmogorov - 1986
7 Sets with small generalized Kolmogorov complexity (context) - Balcazar, Book - 1986
6 Preliminary version appeared (context) - Hitchcock, Lutz et al. - 2003
5 the polynomial time bounded measure of one-truthtable degree.. (context) - Lindner - 1993
4 Hard sets are hard to find - Buhrman, van Melkebeek - 1999
2 ective Fractal Dimension: Foundations and Applications (context) - Hitchcock - 2003
1 Effective strong dimension in algorithmic information and co.. - Athreya, Hitchcock et al. - 2004
1 Small spans in scaled dimension - Hitchcock - 2004
1 Base invariance of feasible dimension (context) - Hitchcock, Mayordomo - 2003
Documents on the same site (http://webdiis.unizar.es/~elvira/research.html): More
Effective Hausdorff Dimension - Mayordomo (2000) (Correct)
Finite-State Dimension - Dai, Lathrop, Lutz, Mayordomo (2001) (Correct)
Scaled Dimension and Nonuniform Complexity - Hitchcock, Lutz, Mayordomo (2003) (Correct)
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