On Irreducibility of the Stream Version of Asymmetric Binary Systems

Hiroshi FUJISAKI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.5   pp.757-768
Publication Date: 2020/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1140
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
ABS (asymmetric binary systems),  irreducibility,  Sturmian sequences,  mechanical words,  

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Summary: 
The interval in ℕ composed of finite states of the stream version of asymmetric binary systems (ABS) is irreducible if it admits an irreducible finite-state Markov chain. We say that the stream version of ABS is irreducible if its interval is irreducible. Duda gave a necessary condition for the interval to be irreducible. For a probability vector (p,1-p), we assume that p is irrational. Then, we give a necessary and sufficient condition for the interval to be irreducible. The obtained conditions imply that, for a sufficiently small ε, if p∈(1/2,1/2+ε), then the stream version of ABS could not be practically irreducible.