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$\mathbb{N}$-algebraicity of zeta functions of sofic-Dyck shifts (1501.05843v2)
Published 23 Jan 2015 in cs.FL
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.