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Scaled Dimension and Nonuniform Complexity (2003)  (Make Corrections)  (1 citation)
John M. Hitchcock, Jack H. Lutz, Elvira Mayordomo



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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

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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)
A Kolmogorov complexity characterization of constructive.. - Mayordomo (2001)   (Correct)

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