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Schnorr Triviality and Its Equivalent Notions

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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.

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Acknowledgements

The author thanks Takayuki Kihara triggering this study and Laurent Bienvenu for crucial discussion on the proof of (iv)⇒(v) of Theorem 5.1. This work was partly supported by GCOE, Kyoto University and JSPS KAKENHI 23740072.

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  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Kenshi Miyabe

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Miyabe, K. Schnorr Triviality and Its Equivalent Notions. Theory Comput Syst 56, 465–486 (2015). https://doi.org/10.1007/s00224-013-9506-8

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