4 research outputs found
Algorithmic analogies to Kamae-Weiss theorem on normal numbers
Open House, ISM in Tachikawa, 2011.7.14統計数理研究所オープンハウス(立川)、H23.7.14ポスター発
Algorithmic randomness and stochastic selection function
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 this paper we consider two types of
algorithmic random sequence; one is ML-random sequences and the other one is
the set of sequences that have maximal complexity rate. Then we show
algorithmic randomness versions of corresponding theorems to the above
classical results.Comment: submitted to CCR2012 special issue. arXiv admin note: text overlap
with arXiv:1106.315