Strong reductions in effective randomness

Authors:
Laurent Bienvenu;Christopher Porter
Affiliations:
LIAFA, CNRS & Universitéé Paris 7, Case 7014, 75205 Paris Cedex 13, France;Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, USA
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

We study generalizations of Demuth's Theorem, which states that the image of a Martin-Lof random real under a tt-reduction is either computable or Turing equivalent to a Martin-Lof 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.