Work

An elementary proof of Bridy's theorem

Year: 2025

Type: article

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.

Source: Finite Fields and Their Applications

DOI: 10.1016/j.ffa.2025.102621

Authors: Eric Rowland, Manon Stipulanti, Reem Yassawi

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,720

Funders: Fonds De La Recherche Scientifique - FNRS, Engineering and Physical Sciences Research Council

Awards: G5018247653, Computing algebraic invariants of symbolic dynamical systems