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A $\lambda$-graph system $\frak L$ is a labeled Bratteli diagram with shiftoperation. It is a generalized notion of finite labeled graph and presents asubshifts. We will study continuous orbit equivalence of one-sided subshiftsand topological conjugacy of two-sided subshifts from the view points ofgroupoids and $C^*$-algebras constructed from $\lambda$-graph systems.

A groupoid approach to $C^*$-algebras associated with $\lambda$-graph systems and continuous orbit equivalence of subshifts