An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Mathematical metaphysics of randomness
Theoretical Computer Science - Special issue Kolmogorov complexity
Ergodic theorems for individual random sequences
Theoretical Computer Science - Special issue Kolmogorov complexity
Effective Randomness for Computable Probability Measures
Electronic Notes in Theoretical Computer Science (ENTCS)
On a definition of random sequences with respect to conditional probability
Information and Computation
Process complexity and effective random tests
Journal of Computer and System Sciences
Monotone conditional complexity bounds on future prediction errors
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
The minimum description length principle in coding and modeling
IEEE Transactions on Information Theory
Redundancy of universal coding, Kolmogorov complexity, and Hausdorff dimension
IEEE Transactions on Information Theory
Randomness Criteria in Terms of -Divergences
IEEE Transactions on Information Theory
On a definition of random sequences with respect to conditional probability
Information and Computation
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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.