Functional Closure Properties of Finite $\mathbb{N}$-weighted Automata

Julian Dörfler; Christian Ikenmeyer

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arXiv · 2404.14245

Functional Closure Properties of Finite $\mathbb{N}$-weighted Automata

Julian Dörfler·Christian Ikenmeyer

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Abstract

We determine all functional closure properties of finite $\mathbb{N}$-weighted automata, even all multivariate ones, and in particular all multivariate polynomials. We also determine all univariate closure properties in the promise setting, and all multivariate closure properties under certain assumptions on the promise, in particular we determine all multivariate closure properties where the output vector lies on a monotone algebraic graph variety.

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Julian Dörfler, Christian Ikenmeyer. 2024-04-22. Functional Closure Properties of Finite $\mathbb{N}$-weighted Automata. https://arxiv.org/abs/2404.14245

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