One-sided topological conjugacy of normal subshifts and gauge actions on the associated C*-algebras

The class of normal subshifts includes irreducible nontrivial topological Markov shifts, irreducible nontrivial sofic shifts, synchronized systems, Dyck shifts, β-shifts, substitution minimal shifts, and so on. We will characterize one-sided topological conjugacy classes of normal subshifts in terms of the associated -algebras and its gauge actions with potentials. In particular, the one-sided topological conjugacy class of irreducible nontrivial sofic shifts are characterized in terms of the simple purely infinite Cuntz-Krieger algebras associated with the matrices of its left Fischer cover graphs and gauge actions with potentials. This generalizes the author's previous result for irreducible nontrivial topological Markov shifts and Cuntz-Krieger algebras with gauge actions.