Semi-groups and graphs for sofic systems
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.
scientific article; zbMATH DE number 4078246
scientific article