• Corpus ID: 17088853

Algorithmic randomness and stochastic selection function

  title={Algorithmic randomness and stochastic selection function},
  author={Hayato Takahashi},
We show algorithmic randomness versions of the two classical theorems on subsequences of normal numbers. One is Kamae-Weiss theorem (Kamae 1973) on normal numbers, which characterize the selection function that preserves normal numbers. Another one is the Steinhaus (1922) theorem on normal numbers, which characterize the normality from their subsequences. In van Lambalgen (1987), an algorithmic analogy to Kamae-Weiss theorem is conjectured in terms of algorithmic randomness and complexity. In… 



Algorithmic Analogies to Kamae-Weiss Theorem on Normal Numbers

  • Hayato Takahashi
  • Mathematics, Computer Science
    Algorithmic Probability and Friends
  • 2011
Different algorithmic analogies to the theorem of Bayesian inference are shown, showing algorithmic randomness and Kolmogorov complexity in subsequences of random numbers.

Ergodic Theorems for Individual Random Sequences

  • V. V'yugin
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1998

The Definition of Random Sequences

On the concept of a random sequence

ly the Kollektiv may be represented by an infinite sequence of points of an appropriate space, the Merkmalraum. Or if the number of possible outcomes of a trial is finite (and it may well be argued

Subsequences of normal sequences

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

Random sequences.

  • 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.

Algorithmic analysis of irrational rotations in a single neuron model

Probability, Statistics and Truth

  • A. A.
  • Mathematics
  • 1940
THIS book is scarcely the philosophical treatise which its title may suggest. It is the written-up version of six lectures on probability and applications, as conceived from von Mises' special

Statistical Problems Related to Irrational Rotations

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

Single Orbit Dynamics

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