Pushdown automata, lambda-graph systems and C*-algebras

A $\lambda$-graph system is a labeled Bratteli diagram with some additional structure, which presents a subshift and yields a $C^*$-algebra. In this paper, we construct a $\lambda$-graph system from a pushdown automaton, such that the accepted language by the automaton coincides with the language of admissible words of the presented subshift by the $\lambda$-graph system. The $\lambda$-graph systems for pushdown automata accepting the languages of Markov-Dyck shifts and sofic-Dyck shifts are presented.