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

TL;DR

This paper characterizes the closure properties of finite d6-weighted automata, including multivariate and polynomial cases, providing a comprehensive understanding of their algebraic and functional capabilities.

Contribution

It fully determines the functional closure properties of finite d6-weighted automata, including multivariate and polynomial cases, under various assumptions and settings.

Findings

All functional closure properties of finite d6-weighted automata are characterized.

Multivariate polynomial automata closure properties are fully described.

Closure properties under promise settings and algebraic graph varieties are established.

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.