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Electronic Colloquium on Computational Complexity

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TR04-030 | 9th March 2004
Nikolay Vereshchagin

Kolmogorov complexity of enumerating finite sets

Solovay has proven that
the minimal length of a program enumerating a set A
is upper bounded by 3 times the absolute value of the
logarithm of the
probability that a random program will enumerate A.
It is unknown whether one can replace the constant
3 by a smaller constant.
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TR04-029 | 7th April 2004
John Hitchcock, Maria Lopez-Valdes, Elvira Mayordomo

Scaled dimension and the Kolmogorov complexity of Turing hard sets

Scaled dimension has been introduced by Hitchcock et al (2003) in order to quantitatively distinguish among classes such as SIZE(2^{a n}) and SIZE(2^{n^{a}}) that have trivial dimension and measure in ESPACE.

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TR04-028 | 19th March 2004
Arfst Nickelsen, Till Tantau, Lorenz Weizsäcker

Aggregates with Component Size One Characterize Polynomial Space

Aggregates are a computational model similar to circuits, but the
underlying graph is not necessarily acyclic. Logspace-uniform
polynomial-size aggregates decide exactly the languages in PSPACE;
without uniformity condition they decide the languages in
PSPACE/poly. As a measure of similarity to boolean circuits we
introduce the parameter component size. We ... more >>>



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