$\mathbb{N}$-algebraicity of zeta functions of sofic-Dyck shifts
Formal Languages and Automata Theory
2017-02-24 v2
Abstract
We prove that the multivariate zeta function of a sofic-Dyck shift is the commutative series of some visibly pushdown language. As a consequence the zeta function of a sofic-Dyck shift is the generating function of a visibly pushdown language and is thus an -algebraic series.
Keywords
Cite
@article{arxiv.1501.05843,
title = {$\mathbb{N}$-algebraicity of zeta functions of sofic-Dyck shifts},
author = {Marie-Pierre Béal and Cǎtǎlin Dima},
journal= {arXiv preprint arXiv:1501.05843},
year = {2017}
}
Comments
This paper has been withdrawn by the authors due to an error in the proof of the main result