Asymptotic density, immunity and randomness
نویسندگان
چکیده
منابع مشابه
Effective Bi-immunity and Randomness
We study the relationship between randomness and effective biimmunity. Greenberg and Miller have shown that for any oracle X, there are arbitrarily slow-growing DNR functions relative to X that compute no MartinLöf random set. We show that the same holds when Martin-Löf randomness is replaced with effective bi-immunity. It follows that there are sequences of effective Hausdorff dimension 1 that...
متن کاملRandomness, Computability, and Density
We study effectively given positive reals (more specifically, computably enumerable reals) under a measure of relative randomness introduced by Solovay [32] and studied by Calude, Hertling, Khoussainov, and Wang [6], Calude [2], Kučera and Slaman [20], and Downey, Hirschfeldt, and LaForte [15], among others. This measure is called domination or Solovay reducibility, and is defined by saying tha...
متن کاملRandomness extraction and asymptotic Hamming distance
We obtain a non-implication result in the Medvedev degrees by studying sequences that are close to Martin-Löf random in asymptotic Hamming distance. Our result is that the class of stochastically bi-immune sets is not Medvedev reducible to the class of sets having complex packing dimension 1.
متن کاملRecovering randomness from an asymptotic Hamming distance
A notion of asymptotic Hamming distance suitable for the study of algorithmic randomness is developed. As an application of this notion, it is shown that there is no fixed procedure that computes a Mises-WaldChurch stochastic set from a complex set. Here a set is complex if its prefixes have Kolmogorov complexity bounded below by an unbounded, nondecreasing computable function.
متن کاملAsymptotic Density for Equivalence
In this paper we study the asymptotic behavior of the fraction of true formulas against all formulas over k propositional variables with equivalence as the only connective in the language. We consider two ways of measuring the asymptotic behavior. In the first case we investigate the size of the tautology fraction of length n against the number of all formulas of length n. The second case is ve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computability
سال: 2015
ISSN: 2211-3576,2211-3568
DOI: 10.3233/com-150040