Semi-groups and graphs for sofic systems
type: Item
instance of: scholarly article
title: Semi-groups and graphs for sofic systems
zbMATH Open document ID: 0659.54037
DOI: 10.1007/BF02772861
author: Selim Tuncel
author: Bruce Kitchens
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A sofic system is a symbolic system which is the image of a shift of finite type under a continuous shift-commuting map. Sofic systems can also be defined using finite semigroups, or using edge-labelled directed graphs. The authors prove a number of theorems relating the dynamics of a sofic system, the algebraic properties of the defining semigroup, and the properties of the defining graph. These results, for the most part, are concerned with covers (pairs \((\Sigma_ A,\phi)\), where \(\Sigma_ A\) is a shift of finite type and \(\phi\) is a continuous shift-commuting map from \(\Sigma_ A\) onto the sofic system), in particular with the degree of a cover (the unique integer k such that \(\phi\) is k-to-one almost everywhere), and with two important technical conditions, called resolving and minimality, on covers.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 20M99
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 4078246
zbMATH Keywords: defining semi-group
zbMATH Keywords: matrix (or graph) theoretic properties
zbMATH Keywords: right and left transition matrices
zbMATH Keywords: sofic graphs
zbMATH Keywords: finite-to-one covers
zbMATH Keywords: minimal left and right resolving covers
zbMATH Keywords: sofic system
zbMATH Keywords: image of a shift of finite type
zbMATH Keywords: continuous shift-commuting map
zbMATH Keywords: edge-labelled directed graphs
MaRDI profile type: Publication
cites work: Topological entropy and equivalence of dynamical systems
cites work: A Note on Minimal Covers for Sofic Systems
cites work: Endomorphisms of irreducible subshifts of finite type
cites work: Sofic systems
cites work: Finite procedures for sofic systems
cites work: Sofic systems and graphs
cites work: Q4185477
cites work: Q3254327
cites work: Endomorphisms and automorphisms of the shift dynamical system
cites work: On sofic systems. I
cites work: Sofic systems and encoding data
cites work: Transmission rates and factors of Markov chains
cites work: An invariant for bounded-to-one factor maps between transitive sofic subshifts
cites work: Intrinsic Markov Chains
cites work: Q3947868
cites work: Subshifts of finite type and sofic systems
cites work: Classification of subshifts of finite type
description: scientific article; zbMATH DE number 4078246