Algorithmic analogies to kamae-Weiss theorem on normal numbers

2011/06/16 by Hayato Takahashi, Takahashi, Hayato
Computer Science · #Algorithms and Data Compression #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1106.3153

openalex publication_date 2011/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Algorithmic randomness and stochastic selection function
• Weak randomness and Kamae's theorem on normal numbers
• Normality, Relativization, and Randomness
• Relations between randomness deficiencies
• Elementary Proof of a Theorem of Jean Ville