Various classes of C*-algebras have been introduced in order to generalize Cuntz-Krieger algebras of topological Markov chains to arbitrary one-sided shift spaces. Among these, labeled graph C*-algebras and lambda-synchronizing lambda-graph C*-algebras are appropriate extensions connecting the irreducibility of shift spaces and the simplicity of C*-algebras. A recent result shows that the labeled graph C*-algebra of the Cantor minimal subshift is isomorphic to the crossed product C*-algebra. In this talk, we introduce a crossed product C*-algebras of a two sided shift space and generalized Cuntz-Krieger algebras of a one-sided shift space, and we investigate the similarity between two classes.