Systèmes codés. (Coded systems)
type: Item
instance of: scholarly article
title: Systèmes codés. (Coded systems)
zbMATH Open document ID: 0601.68056
DOI: 10.1016/0304-3975(86)90108-8
published in: Theoretical Computer Science
publication date: 1986-01-01T00:00:00Z
review text: By definition, coded systems are those subshifts on a finite alphabet A which are generated by a strongly connected graph with a denumerable set of vertices (whereas sofic systems are generated by a finite graph). Now, letting F be any set of finite sequences on A, it is proved that the closure S of the set \(F^{\infty}\) of doubly infinite sequences that may be cut into blocks belonging to F is always coded - the converse being obvious. Therefore, coded systems are stable under factor maps (homomorphisms). Synchronizing systems are coded systems for which a canonical family of generating sets F exists. The structure of the set of ergodic measures on \(F^{\infty}\) is roughly the same as that of the set of all ergodic measures on a sofic system, and some further results are proved for synchronizing systems: but in many instances, no measure on \(F^{\infty}\) reaches the topological entropy of S. Various examples are discussed in the end. Since this paper was written down, W. Krieger has found out a simple topological characterization of coded systems, and proved that synchronizing systems are stable under conjugacy maps; A. Bertrand-Mathis has used results on coded systems for the study of \(\beta\)-shifts.
Mathematics Subject Classification ID: 68Q45
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 3970131
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: coded systems
zbMATH Keywords: subshifts on a finite alphabet
zbMATH Keywords: strongly connected graph
zbMATH Keywords: sofic systems
zbMATH Keywords: Synchronizing systems
zbMATH Keywords: generating sets
zbMATH Keywords: ergodic measures
zbMATH Keywords: topological entropy
author: François Blanchard
author: Georges Hansel
MaRDI profile type: Publication
full work available at URL: 0304-3975(86)90108-8
OpenAlex ID: W4213194827
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description: scientific article; zbMATH DE number 3970131