# A Robust Class of Linear Recurrence Sequences

## TL;DR

This paper introduces poly-rational sequences, a robust subclass of linear recurrence sequences characterized by rational expressions, automata, and eigenvalue properties, expanding understanding of their algebraic and automata-theoretic structure.

## Contribution

The paper defines poly-rational sequences and demonstrates their equivalence across multiple formal frameworks, highlighting their robustness and algebraic properties.

## Key findings

- Poly-rational sequences are closed under sum and product.
- They can be characterized by weighted automata and formal series.
- Eigenvalues of these sequences are roots of rational numbers.

## Abstract

We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register automata, rational formal series, and linear recurrence sequences whose eigenvalues are roots of rational numbers.