Effective randomness, strong reductions and Demuth's theorem

Laurent Bienvenu (1) , Christopher Porter (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 Department of Mathematics

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 statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure.

Mots clés: Demuth's theorem; computable analysis; Algorithmic randomness

Domaines: Logique [math.LO]

Laurent Bienvenu, Christopher Porter. Effective randomness, strong reductions and Demuth's theorem. 2011. ⟨hal-00630308v2⟩