# Algorithmic Analogies to Kamae-Weiss Theorem on Normal Numbers

@article{Takahashi2011AlgorithmicAT,
title={Algorithmic Analogies to Kamae-Weiss Theorem on Normal Numbers},
author={Hayato Takahashi},
journal={ArXiv},
year={2011},
volume={abs/1106.3153}
}
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.
3 Citations
Two types of algorithmic random sequence are considered; one is ML-random sequences and the other one is the set of sequences that have maximal complexity rate.
• D. Dowe
• Psychology
Algorithmic Probability and Friends
• 2011
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

## References

SHOWING 1-10 OF 17 REFERENCES

In this paper, we characterize a set of indices τ={τ(0)<τ(1)<…} such that forany normal sequence (α(0), α(1),…) of a certain type, the subsequence (α(τ(0)), α(τ(1)),…) is a normal sequence of the
• 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.
• Mathematics
• 2006
Let $$\xi_i := \lfloor i\alpha + \beta\rfloor - \lfloor (i - 1)\alpha+\beta\rfloor\quad(i=1,2,\ldots,m)$$ be random variables as functions of β in the probability space [0,1) with the Lebesgue
What is single orbit dynamics Topological dynamics Invariant measures, ergodicity and unique ergodicity Ergodic and uniquely ergodic orbits Translation invariant graphs and recurrence Patterns in

### Normal sequences as collectives

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