منابع مشابه
Characterizing strong randomness via Martin-Löf randomness
We introduce two methods to characterize strong randomness notions via Martin-Löf randomness. By applying these methods, we investigate ∅′-Schnorr randomness.
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We study generalizations of Demuth’s Theorem, which states that the image of a Martin-Löf random real under a tt-reduction is either computable or Turing equivalent to a Martin-Löf random real. We show that Demuth’s Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the stat...
متن کاملEffective randomness, strong reductions and Demuth’s theorem
We study generalizations of Demuth’s Theorem, which states that the image of a Martin-Löf random real under a tt-reduction is either computable or Turing equivalent to a Martin-Löf random real. We show that Demuth’s Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the stat...
متن کاملDo Most Strong Deenitions of Randomness Exist? Ecole Normale Supérieure De Lyon Do Most Strong Deenitions of Randomness Exist? Do Most Strong Deenitions of Randomness Exist?
The goal of our paper is to propose a way to obtain more re ned de nitions of randomness than the notions known so far e g Martin L of randomness We show that a perfect de nition of randomness based on provability does not exist We then weaken our require ments on the de nition by replacing provability by consistency and obtain a formula that de nes a set of random sequences that ful lls rather...
متن کاملStrong Kochen-Specker theorem and incomputability of quantum randomness
The Kochen-Specker theorem shows the impossibility for a hidden variable theory to consistently assign values to certain (finite) sets of observables in a way that is noncontextual and consistent with quantum mechanics. If we require noncontextuality, the consequence is that many observables must not have pre-existing definite values. However, the Kochen-Specker theorem does not allow one to de...
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ژورنال
عنوان ژورنال: Physics Today
سال: 2007
ISSN: 0031-9228,1945-0699
DOI: 10.1063/1.2812103