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» Randomness and the linear degrees of computability
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APAL
2007
88views more  APAL 2007»
13 years 4 months ago
Randomness and the linear degrees of computability
We show that there exists a real α such that, for all reals β, if α is linear reducible to β (α ≤ β, previously denoted α ≤sw β) then β ≤T α. In fact, every random ...
Andrew E. M. Lewis, George Barmpalias
STOC
2006
ACM
116views Algorithms» more  STOC 2006»
14 years 4 months ago
Linear degree extractors and the inapproximability of max clique and chromatic number
: We derandomize results of H?astad (1999) and Feige and Kilian (1998) and show that for all > 0, approximating MAX CLIQUE and CHROMATIC NUMBER to within n1are NP-hard. We furt...
David Zuckerman
CIE
2009
Springer
13 years 11 months ago
Lowness for Demuth Randomness
We show that every real low for Demuth randomness is of hyperimmune-free degree.
Rod Downey, Keng Meng Ng
APAL
2010
125views more  APAL 2010»
13 years 4 months ago
The computable Lipschitz degrees of computably enumerable sets are not dense
The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truthtable reducibility [6]. This reducibility measures both t...
Adam R. Day
FOCS
2004
IEEE
13 years 8 months ago
Randomly Coloring Constant Degree Graphs
We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree . We prove that, for every > 0, the d...
Martin E. Dyer, Alan M. Frieze, Thomas P. Hayes, E...