Algorithmic randomness and monotone complexity on product space

Hayato Takahashi

doi:10.1016/j.ic.2010.10.003

Hayato Takahashi

Open Access

https://doi.org/10.1016/j.ic.2010.10.003

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Journal: Information and Control	Publication Date: Oct 30, 2010
Citations: 20	License type: elsevier-specific: oa user license

Affiliation: The Institute of Statistical Mathematics

Abstract

We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen’s theorem for correlated probability, classification of random sets by likelihood ratio tests, decomposition of complexity and independence, and Bayesian statistics for individual random sequences. Formerly Lambalgen’s theorem for correlated probability is shown under a uniform computability assumption in [H. Takahashi Inform. Compt. 2008]. In this paper we show the theorem without the assumption.

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