Structured audio, Kolmogorov complexity, and generalized audio coding

2001 ◽  
Vol 9 (8) ◽  
pp. 914-931 ◽  
Author(s):  
E.D. Scheirer
Keyword(s):  
Kolmogorov Complexity ◽  
Audio Coding ◽  
Structured Audio

Computable Følner monotilings and a theorem of Brudno

2020 ◽  
pp. 1-28
Author(s):  
NIKITA MORIAKOV
Keyword(s):  
Kolmogorov Complexity

Abstract A theorem of Brudno says that the Kolmogorov–Sinai entropy of an ergodic subshift over $\mathbb {N}$ equals the asymptotic Kolmogorov complexity of almost every word in the subshift. The purpose of this paper is to extend this result to subshifts over computable groups that admit computable regular symmetric Følner monotilings, which we introduce in this work. For every $d \in \mathbb {N}$ , the groups $\mathbb {Z}^d$ and $\mathsf{UT}_{d+1}(\mathbb {Z})$ admit computable regular symmetric Følner monotilings for which the required computing algorithms are provided.

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