Topology automaton and conformal dimension of post-critical-finite self-similar sets

In this paper, we use a class of finite state automata, called topology automaton, to study the metric classification of a special class of post-critically finite self-similar sets. As an application, we prove that the conformal dimension of post-critically finite self-similar dendrites and fractal gasket with connected component is 1.
Comment: 38 pages, 11 figures, 27 references