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From index sets to randomness in ∅n: random reals and possibly infinite computations part II

Published online by Cambridge University Press:  12 March 2014

Verónica Becher
Affiliation:
Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Conicet, Argentina, E-mail: vbecher@dc.uba.ar
Serge Grigorieff
Affiliation:
Liafa, Université Paris7 & CNRS, France, E-mail: seg@liafa.jussieu.fr

Abstract

We obtain a large class of significant examples of n-random reals (i.e., Martin-Löf random in oracle ∅(n−1)) à la Chaitin. Any such real is defined as the probability that a universal monotone Turing machine performing possibly infinite computations on infinite (resp. finite large enough, resp. finite self-delimited) inputs produces an output in a given set . In particular, we develop methods to transfer many-one completeness results of index sets to n-randomness of associated probabilities.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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