S. A. Fenner. Gales and supergales are equivalent for defining constructive Hausdor# dimension. Technical Report cs.CC/02080. Home/Search Document Not in Database Summary Related Articles Check |
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The Arithmetical Complexity of Dimension and Randomness - Hitchcock, Lutz, Terwijn (2003) (1 citation) (Correct)
....is called constructive if it is lower semicomputable. The constructive dimension of a class cdim(A) inf # # (2.3) and the constructive dimension of an individual sequence A dim(A) cdim( A ) Supergales can be equivalently used in place of gales in both (2.2) and (2. 3) [13, 9, 4]. Constructive dimension has some remarkable properties. For example, Lutz [14] showed that for any class A, cdim(A) sup A#A dim(A) 2.4) Also, Mayordomo [16] established an strong connection with Kolmogorov complexity: for any A C, dim(A) lim inf n , 2.5) where K(A # n) is the ....
S. A. Fenner. Gales and supergales are equivalent for defining constructive Hausdor# dimension. Technical Report cs.CC/02080.
Effective Strong Dimension, Algorithmic.. - Athreya.. (2004) (Correct)
....of Hausdor# dimension, including constructive, computable, polynomial space, polynomial time, and finite state dimensions. Work by several investigators has already used these e#ective dimensions to illuminate a variety of topics in algorithmic information theory and computational complexity [20, 21, 1, 7, 27, 16, 15, 11, 13, 14, 10]. See [26] for a survey of some of these results. This work has also underscored and renewed the importance of earlier work by Ryabko [28, 29, 30, 31] Staiger [37, 38, 39] and Cai and Hartmanis [5] relating Kolmogorov complexity to classical Hausdor# dimension. See Section 6 of [21] for a ....
S. A. Fenner. Gales and supergales are equivalent for defining constructive Hausdor# dimension. Technical Report cs.CC/02080.
Effective Fractal Dimension Bibliography - Hitchcock (Correct)
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S. A. Fenner. Gales and supergales are equivalent for defining constructive Hausdor# dimension. Technical Report cs.CC/02080.
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