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The limit behavior of a transient Markov chain can be described by its Martin boundary together with an elegant discrete potential theory.It is known that in fractal theory,a self-similar set K has a symbolic representation.In this talk we will introduce certain class of Markov chains on the symbolic spaces.Our objective is to identify the Martin boundary with K.This way we can induce harmonic structure and Dirichlet form on self-similar sets.The study relates to the current interest on the analysis on fractals.