$\mathbb{N}$-algebraicity of zeta functions of sofic-Dyck shifts

Marie-Pierre Béal; Cǎtǎlin Dima

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arXiv · 1501.05843

$\mathbb{N}$-algebraicity of zeta functions of sofic-Dyck shifts

Marie-Pierre Béal·Cǎtǎlin Dima

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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 $\mathbb{N}$-algebraic series.

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BibTeX RIS

Marie-Pierre Béal, Cǎtǎlin Dima. 2017-02-23. $\mathbb{N}$-algebraicity of zeta functions of sofic-Dyck shifts. https://arxiv.org/abs/1501.05843

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