IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Regular Section
Complexity Oscillations in Random Reals
ChenGuang LIUKazuyuki TANAKA
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JOURNAL FREE ACCESS

2008 Volume E91.D Issue 10 Pages 2517-2518

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Abstract

The C-oscillation due to Martin-Löf shows that {α|∀n[C(α↑n)≥n-O(1)]}=0, which also follows {α|∀n[K(α↑n)≥n+K(n)-O(1)]}=0. By generalizing them, we show that there does not exist a real α such that ∀n(K(α↑n)≥nK(n)-O(1))for any λ>0.

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© 2008 The Institute of Electronics, Information and Communication Engineers
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