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

TL;DR

This paper constructs lambda-graph systems from pushdown automata, linking formal language theory with operator algebras, and demonstrates their application to specific classes of shift spaces.

Contribution

It introduces a method to derive lambda-graph systems from pushdown automata, connecting automata theory with C*-algebras and subshift presentations.

Findings

Lambda-graph systems can be constructed from pushdown automata.

The accepted languages match the admissible words of the subshift.

Applications to Markov-Dyck and sofic-Dyck shifts are provided.

Abstract

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.