Sofic-Dyck shifts

TL;DR

This paper introduces sofic-Dyck shifts, a new class of sequence shifts characterized by unambiguous context-free languages, and establishes their equivalence with visibly pushdown languages, providing a zeta function expression.

Contribution

It defines sofic-Dyck shifts, extending Markov-Dyck shifts, and proves their equivalence to visibly pushdown languages, along with deriving their zeta functions.

Findings

Sofic-Dyck shifts extend Markov-Dyck shifts.

They are characterized by unambiguous context-free languages.

The zeta function for these shifts is explicitly derived.

Abstract

We define the class of sofic-Dyck shifts which extends the class of Markov-Dyck shifts introduced by Inoue, Krieger and Matsumoto. Sofic-Dyck shifts are shifts of sequences whose finite factors form unambiguous context-free languages. We show that they correspond exactly to the class of shifts of sequences whose sets of factors are visibly pushdown languages. We give an expression of the zeta function of a sofic-Dyck shift.