Poly-rational sequences are exactly the sequences of polynomially ambiguous weighted automata, of copyless cost-register automata, and of linear recurrences whose eigenvalues are roots of rational numbers.
Probabilistic automata of bounded ambiguity
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A Robust Class of Linear Recurrence Sequences
Poly-rational sequences are exactly the sequences of polynomially ambiguous weighted automata, of copyless cost-register automata, and of linear recurrences whose eigenvalues are roots of rational numbers.