Written under supervision by Prof. dr. G.L.M. Cornelissen with dr. V.Z.Karemaker as a second reader.
Abstract: A well-known theorem infinite automata theory is the following: a power series over a finite field isalgebraic if and only if its coefficient sequence is automatic. This result isknown as Christol's Theorem. In a recent paper, Bridy proved new bounds for thenumber of states for the automaton of an algebraic power series. Although thesebounds are sharp in some specific cases, there are many examples of algebraicpower series with automata which are far smaller than expected from the bounds.After introducing the theory of function fields and automata, we study Bridy'sbounds in more detail. We use an experimental approach to study the automata ofseveral families of algebraic power series. Lastly, we provide a MAGMAprocedure which for a given irreducible polynomial over a finite field computesall power series solutions and their automata.
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