John M. Hitchcock, Jack H. Lutz, Elvira Mayordomo  Home/Search
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Abstract: Resource-bounded dimension is a complexity-theoretic extension of classical Hausdor # dimension introduced by Lutz (2000) in order to investigate the fractal structure of sets that have resource-bounded measure 0. For example, while it has long been known that the Boolean circuit-size complexity class SIZE has measure 0 in ESPACE for all 0 1, we now know that SIZE has dimension # in ESPACE for all 0 1. The present paper furthers this program by developing a natural... (Update)
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BibTeX entry: (Update)
@misc{ hitchcock-scaled,
author = "John M. Hitchcock and Jack H. Lutz and Elvira Mayordomo",
title = "Scaled Dimension and Nonuniform Complexity",
url = "citeseer.ist.psu.edu/article/hitchcock03scaled.html" }
Citations (may not include all citations):152 Fractal Geometry: Mathematical Foundations and Applications (context) - Falconer - 1990
142 Almost everywhere high nonuniform complexity - Lutz - 1992
47 Zufalligkeit und Wahrscheinlichkeit (context) - Schnorr
35 Cambridge University Press (context) - Rogers, Measures - 1998
35 Etude Critique de la Notion de Collectif (context) - Ville - 1939
33 A unified approach to the definition of random sequences (context) - Schnorr - 1971
31 Dimension in complexity classes - Lutz - 2003
30 Resource-bounded measure (context) - Lutz - 1998
17 Klassifikation der Zufallsgesetze nach Komplexitat und Ordnu.. (context) - Schnorr - 1970
15 dimension in exponential time (context) - Ambos-Spies, Merkle et al. - 2001
14 Process complexity and e#ective random tests (context) - Schnorr - 1973
12 Theorie de l'Addition des Variables Aleatoires (context) - Levy - 1937
12 Dimension und ausseres Mass (context) - Hausdor - 1919
9 Completeness and weak completeness under polynomial-size cir.. - Juedes, Lutz - 1996
8 MAXSAT is exponentially hard to approximate if NP ha positiv.. - SAT, hard et al. - 2002
[Article contains additional citations not shown here]
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