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

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