Demuth randomness and computational complexity
نویسندگان
چکیده
منابع مشابه
Demuth randomness and computational complexity
Demuth tests generalize Martin-Löf tests (Gm)m∈N in that one can exchange the m-th component for a computably bounded number of times. A set Z ⊆ N fails a Demuth test if Z is in infinitely many final versions of the Gm. If we only allow Demuth tests such that Gm ⊇ Gm+1 for each m, we have weak Demuth randomness. We show that a weakly Demuth random set can be high, yet not superhigh. Next, any c...
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We extend our work on difference randomness. Each component of a difference test is a Boolean combination of two r.e. open sets; here we consider tests in which the k component is a Boolean combination of g(k) r.e. open sets for a given recursive function g. We use this method to produce an alternate characterization of weak Demuth randomness in terms of these tests and further show that a real...
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A set A ⊆ N is called a base for Demuth randomness if some set Y ≥T A is Demuth random relative to A. We show that there is an incomputable c.e. base for Demuth randomness, and each base for Demuth randomness is strongly jump-traceable.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2011
ISSN: 0168-0072
DOI: 10.1016/j.apal.2011.01.004