Randomness on computable probability spaces - A dynamical point of view

Peter Gacs, Mathieu Hoyrup, Cristobal Rojas

Resultado de la investigación: Contribución a los tipos de informe/libroContribución a la conferencia

9 Citas (Scopus)

Resumen

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.

Idioma originalInglés
Título de la publicación alojadaSTACS 2009 - 26th International Symposium on Theoretical Aspects of Computer Science
Páginas469-480
Número de páginas12
Volumen3
EstadoPublicada - 2009
Evento26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009 - Freiburg, Alemania
Duración: 26 feb 200928 feb 2009

Otros

Otros26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009
PaísAlemania
CiudadFreiburg
Período26/02/0928/02/09

Áreas temáticas de ASJC Scopus

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Citar esto

Gacs, P., Hoyrup, M., & Rojas, C. (2009). Randomness on computable probability spaces - A dynamical point of view. En STACS 2009 - 26th International Symposium on Theoretical Aspects of Computer Science (Vol. 3, pp. 469-480)