Randomness on Computable Probability Spaces - A Dynamical Point of View

Peter Gacs 1 Mathieu Hoyrup 2, 3 Cristobal Rojas 2, 4
1 Boston University - Computer Science Department [Boston]
2 ENS Paris - École normale supérieure - Paris
3 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
4 CREA - Centre de recherche en épistémologie appliquée
Abstract : We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the statistical behavior of the system (Birkhoff's pointwise ergodic theorem). We prove that a point is Schnorr random if and only if it is typical for every mixing computable dynamics. To prove the result we develop some tools for the theory of computable probability spaces (for example, morphisms) that are expected to have other applications.
Keywords : Schnorr Randomness Birkhoff's ergodic theorem computable measures
Type de document :
Communication dans un congrès
Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.469-480, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science
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  • ARXIV : 0902.1939

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Peter Gacs, Mathieu Hoyrup, Cristobal Rojas. Randomness on Computable Probability Spaces - A Dynamical Point of View. Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.469-480, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science. 〈inria-00360519〉

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