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arXiv · 2308.10977

An elementary proof of Bridy's theorem

Eric Rowland·Manon Stipulanti·Reem Yassawi
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Abstract

Christol's theorem states that a power series with coefficients in a finite field is algebraic if and only if its coefficient sequence is automatic. A natural question is how the size of a polynomial describing such a sequence relates to the size of an automaton describing the same sequence. Bridy used tools from algebraic geometry to bound the size of the minimal automaton for a sequence, given its minimal polynomial. We produce a new proof of Bridy's bound by embedding algebraic sequences as diagonals of rational functions.

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Eric Rowland, Manon Stipulanti, Reem Yassawi. 2023-08-21. An elementary proof of Bridy's theorem. https://doi.org/10.1016/j.ffa.2025.102621

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