Algorithmic complexity of β-expansions and application to A/D conversion
Abstract
We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and β-expansions. These relationships allow to develop intuitions on the complexity behavior of β-expansions, and raise problems related to compressibility of binary sequences generated in the context of A/D conversion relying on β-expansions. Our last contribution is to solve these problems.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.