ℕ-algebraicity of zeta functions of sofic-Dyck shifts

2015/01/23 by Marie-Pierre Béal, Béal, Marie-Pierre, Cătălin Dima +1
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1501.05843

openalex publication_date 2015/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-algebraic series.

Citations

• Subshifts from sofic shifts and Dyck shifts, zeta functions and topological entropy
• The Zeta function, Periodic Points and Entropies of the Motzkin Shift

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