K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210--217, 2001. 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)
....of Dimension and Randomness John M. Hitchcock # Jack H. Lutz Sebastiaan A. Terwijn # Abstract Constructive dimension and constructive strong dimension are e#ectivizations of the Hausdor# and packing dimensions, respectively. Each infinite binary sequence A is assigned a dimension [0, 1] and a strong dimension Dim(A) 0, 1] Let DIM str be the classes of all sequences of dimension # and of strong dimension #, respectively. We show that DIM 2 , and that for all # (0, 1] 3 . To classify the strong dimension classes, we use a more powerful e#ective Borel ....
....M. Hitchcock # Jack H. Lutz Sebastiaan A. Terwijn # Abstract Constructive dimension and constructive strong dimension are e#ectivizations of the Hausdor# and packing dimensions, respectively. Each infinite binary sequence A is assigned a dimension [0, 1] and a strong dimension Dim(A) [0, 1]. Let DIM str be the classes of all sequences of dimension # and of strong dimension #, respectively. We show that DIM 2 , and that for all # (0, 1] 3 . To classify the strong dimension classes, we use a more powerful e#ective Borel hierarchy where a co enumerable predicate is ....
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210-- 217, 2001.
The Frequency of Difficult Instances for MaxClique Approximation .. - Hitchcock (Correct)
.... 11. As #(w, b) is exactly computable in time O( w ) the proposition holds. The following proposition allows us to only be concerned with individual languages when investigating the dimension of a class. This proposition is similar to one given by Ambos Spies, Merkle, Stephan, and Reimann [2]. be a class of languages and let r N. If for each A there is some predictor #A computable in O(n ) time such that (# A , A) s, then dim p (C) s. Analogously, if for each A there is a predictor #A computable in O(n ) time satisfying str (# A , A) s, then s. ....
K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210-- 217, 2001. 16
Small Spans in Scaled Dimension - Hitchcock (2004) (Correct)
....1] and is denoted by dim(C D) If dim(C 1, then (C = 0, but the converse may fail. This means that resource bounded dimension is capable of quantitatively distinguishing among the measure 0 sets. With regard to the measure 0 sets in Theorem 1. 1, Ambos Spies, Merkle, Reimann, and Stephan [2] proved the following. Theorem 1.2. Ambos Spies, Merkle, Reimann, and Stephan [2] For every A E) In particular, as dim(E E) 1, the m complete degree for E has dimension 1 within E. This implies that replacing by dim in Theorem 1.1 makes the statement for E no longer true. In ....
....may fail. This means that resource bounded dimension is capable of quantitatively distinguishing among the measure 0 sets. With regard to the measure 0 sets in Theorem 1.1, Ambos Spies, Merkle, Reimann, and Stephan [2] proved the following. Theorem 1.2. Ambos Spies, Merkle, Reimann, and Stephan [2]) For every A E) In particular, as dim(E E) 1, the m complete degree for E has dimension 1 within E. This implies that replacing by dim in Theorem 1.1 makes the statement for E no longer true. In other words, there is no analogue of the small span theorem for dimension in E. ....
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210-- 217, 2001.
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 ....
....nonnegative integers) the set Q of rational numbers, the set R of real numbers, and the set of nonnegative reals. All logarithms in this paper are base 2. We use the slow growing function log # n = min j n , where t 0 = 0 and t j 1 = 2 , and Shannon s binary entropy function : [0, 1] [0, 1] defined by = # log (1 #) log 1 , where 0 log = 0. A language, or decision problem, is a set A 1 # . We usually identify a language A with it characteristic sequence #A C defined by #A [n] if s n A then 1 else 0, where s 0 = #, s 1 = 0, s 2 = 1, s 3 = 00, ....
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210-- 217, 2001.
Infinitely-Often Autoreducible Sets - Beigel, Fortnow, Stephan (2003) (2 citations) Self-citation (Stephan) (Correct)
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Klaus Ambos-Spies, Wolfgang Merkle, Jan Reimann and Frank Stephan. Hausdor# dimension in exponential time. Proceedings Sixteenth Annual IEEE Conference on Computational Complexity, IEEE Computer Society, 210--217, 2001.
Effective Randomness - Merkle (2004) Self-citation (Merkle) (Correct)
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Ambos-Spies, K., Merkle, W., Reimann, J., and Stephan, F. Hausdor dimension in exponential time. In Proceedings of the 16th Annual IEEE Conference on Computational Complexity (Chicago, Illinois, USA, 2000), IEEE Computer Society, ACM SIGACT, EATCS, IEEE Computer Society Press, pp. 210-217.
Infinitely-Often Autoreducible Sets - Beigel, Fortnow, Stephan (2003) (2 citations) Self-citation (Stephan) (Correct)
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Klaus Ambos-Spies, Wolfgang Merkle, Jan Reimann and Frank Stephan. Hausdor dimension in exponential time. Proceedings Sixteenth Annual IEEE Conference on Computational Complexity, IEEE Computer Society, 210-217, 2001.
Scaled dimension and the Kolmogorov complexity of.. - Hitchcock.. (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210--217, 2001.
Some Recent Progress in Algorithmic Randomness - Downey (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan, Hausdor# Dimension in Exponential Time, Computational Complexity 2001, 210-217, IEEE Computer Society, 2001.
Scaled Dimension and Nonuniform Complexity - Hitchcock, Lutz, Mayordomo (2003) (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, F. Stephan, Hausdor# dimension in exponential time, in: Proceedings of the 16th IEEE Conference on Computational Complexity, 2001, pp. 210--217. 29
Effective Fractal Dimensions - Lutz (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210{ 217, 2001.
Effective Fractal Dimension Bibliography - Hitchcock (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210-- 217. IEEE Computer Society, 2001.
Prediction and Dimension - Fortnow, Lutz (2003) (1 citation) (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor# dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210--217, 2001.
Complexity and Randomness - Terwijn (2003) (1 citation) (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan, Hausdor# Dimension in Exponential Time, Computational Complexity 2001.
Effective Dimension Bibliography - Hitchcock (Correct)
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K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdor dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210-217, 2001.
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