Every 2-random real is Kolmogorov random
Copyright policy )Every 2-random real is Kolmogorov random
Abstract.We study reals with infinitely many incompressible prefixes. Call A ∈ 2ωKolmogorov random if . where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by Martin-Löf. Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse—proved by Nies. Stephan and Terwijn [11]—this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of 2-randomness.
- Victoria University Australia
- Victoria University Uganda
Kolmogorov random sequence, Applications of computability and recursion theory, Kolmogorov complexity, Martin-Löf random sequence, Kolmogorov randomness, Algorithmic information theory (Kolmogorov complexity, etc.)
Kolmogorov random sequence, Applications of computability and recursion theory, Kolmogorov complexity, Martin-Löf random sequence, Kolmogorov randomness, Algorithmic information theory (Kolmogorov complexity, etc.)
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