English

$\mathbb{N}$-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 N\mathbb{N}-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This paper has been withdrawn by the authors due to an error in the proof of the main result