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Schnorr triviality is equivalent to being a basis for tt-Schnorr randomness

Presented by: 
K Miyabe Kyoto University
Date: 
Monday 2nd July 2012 - 15:00 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
We present some new characterizations of Schnorr triviality. Schnorr triviality is defined using complexity via a computable measure machine, with which Schnorr randomness has a characterization. Since we have a characterization of Schnorr randomness via decidable prefix-free machine, we also have a characterization of Schnorr triviality using complexity via a decidable prefix-free machine. It should be noted that numerous characterizations of Schnorr triviality have the following form: for any computable object, there exists another computable object such that the real is in some object. By defining a basis for Schnorr randomness in a similar manner, we can show the equivalence to Schnorr triviality while Franklin and Stephan (2010) showed that there exists a Schnorr trivial set that is not truth-table reducible to any Schnorr random set.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons