Algorithmic Analogies to Kamae-Weiss Theorem on Normal Numbers

  title={Algorithmic Analogies to Kamae-Weiss Theorem on Normal Numbers},
  author={Hayato Takahashi},
In this paper we study subsequences of random numbers. In Kamae (1973), selection functions that depend only on coordinates are studied, and their necessary and sufficient condition for the selected sequences to be normal numbers is given. In van Lambalgen (1987), an algorithmic analogy to the theorem is conjectured in terms of algorithmic randomness and Kolmogorov complexity. In this paper, we show different algorithmic analogies to the theorem. 

Algorithmic randomness and stochastic selection function

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This piece is an introduction to the proceedings of the Ray Solomonoff 85th memorial conference, paying tribute to the works and life of Ray Solomonoff, and mentioning other papers from the



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  • 1998

Algorithmic analysis of irrational rotations in a single neuron model

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  • W. Fitch
  • Computer Science
    Journal of molecular biology
  • 1983
It is shown that biased nearest-neighbor frequencies can significantly affect the probability of observing a given result and methods for producing random sequences according to these decisions are given.

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  • In Proc. Symp. on Topological Dynamics and Ergodic Theory. Univ. of Kentucky,
  • 1971