Theory of Computing Systems

, Volume 56, Issue 3, pp 465–486 | Cite as

Schnorr Triviality and Its Equivalent Notions

Article

Abstract

We give some characterizations of Schnorr triviality. In concrete terms, we introduce a reducibility related to decidable prefix-free machines and show the equivalence with Schnorr reducibility. We also give a uniform-Schnorr-randomness version of the equivalence of LR-reducibility and LK-reducibility. Finally we prove a base-type characterization of Schnorr triviality.

Keywords

Algorithmic randomness Schnorr randomness Schnorr triviality Uniform relativization Lowness for uniform Schnorr randomness 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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