On the construction of effectively random sets
Abstract.We present a comparatively simple way to construct Martin-Löf random and rec-random sets with certain additional properties, which works by diagonalizing against appropriate martingales. Reviewing the result of Gács and Kučera, for any given set X we construct a Martin-Löf random set from which X can be decoded effectively.By a variant of the basic construction we obtain a rec-random set that is weak truth-table autoreducible and we observe that there are Martin-Löf random sets that are computably enumerable self-reducible. The two latter results complement the known facts that no rec-random set is truth-table autoreducible and that no Martin-Löf random set is Turing-autoreducible [8, 24].
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2011 ◽
Vol 19
(05)
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pp. 799-823
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1994 ◽
Vol 4
(3)
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pp. 273-290
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2000 ◽
Vol 32
(01)
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pp. 86-100
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2010 ◽
Vol 29-32
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pp. 1252-1257
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