منابع مشابه
Comparing notions of randomness
It is an open problem in the area of computable randomness whether Kolmogorov-Loveland randomness coincides with Martin-Löf randomness. Joe Miller and André Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of partial permutation randomness is still weaker than Martin-Löf randomness.
متن کاملComplexity of Randomness Notions
Schnorr famously proved that Martin-Löf-randomness of a sequence A can be characterised via the complexity of A’s initial segments. Nies, Stephan and Terwijn as well as independently Miller showed that Kolmogorov randomness coincides with Martin-Löf randomness relative to the halting problem K; that is, a set A is Martin-Löf random relative to K iff there is no function f such that for all m an...
متن کاملRandomness notions and partial relativization
We study weak 2 randomness, weak randomness relative to ∅′ and Schnorr randomness relative to ∅′. One major theme is characterizing the oracles A such that ML[A] ⊆ C, where C is a randomness notion and ML[A] denotes the Martin-Löf random reals relative to A. We discuss the connections with LR-reducibility and also study the reducibility associated with weak 2randomness.
متن کاملInitial Segment Complexities of Randomness Notions
Schnorr famously proved that Martin-Löf-randomness of a sequence A can be characterised via the complexity of A’s initial segments. Nies, Stephan and Terwijn as well as independently Miller showed that Kolmogorov randomness coincides with Martin-Löf randomness relative to the halting problem K; that is, a set A is Martin-Löf random relative to K iff there is no function f such that for all m an...
متن کاملSeparations of Non-monotonic Randomness Notions
In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Martin-Löf randomness and computable randomness. The latter notion was introduced by Schnorr and is rather natural: an infinite binary sequence is computably random if no total computable strategy succeeds on it by bettin...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2010
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2009.09.036