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Abstract: Solovay showed that there are noncomputable reals # such that H(# ) +O(1), where H is prefix-free Kolmogorov complexity. Such H-trivial reals are interesting due to the connection between algorithmic complexity and effective randomness. We give a new, easier construction of an H-trivial real. We also analyze various computability-theoretic properties of the H-trivial reals, showing for example that no H-trivial real can compute the halting problem (which means that our construction of an... (Update)
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...to a constant) namely #nK(X # n) K(n) O(1) Let denote this class of reals. contains nonrecursive r.e. sets and is closed under (see [2] for proofs and more references) In this paper we show that, for each low r.e. B,there is an r.e. A #Ksuch T B. In Nies [7] we prove...
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BibTeX entry: (Update)
R. G. Downey, D. R. Hirschfeldt, A. Nies, F. Stephan, Trivial reals, In Electronic Notes in Theoretical Computer Science (ENTCS), 2002. http://citeseer.ist.psu.edu/article/downey02trivial.html More
@article{ downey02trivial,
author = "R. Downey and D. Hirschfeldt and A. Nies and F. Stephan",
title = "Trivial reals",
journal = "Electronic Notes in Theoretical Computer Science (ENTCS)",
volume = "66",
number = "1",
year = "2002",
url = "citeseer.ist.psu.edu/article/downey02trivial.html" }
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