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math.AC2004
Finite automata and algebraic extensions of function fields
Kiran S. Kedlaya
We give an automata-theoretic description of the algebraic closure of the rational function field F_q(t) over a finite field, generalizing a result of Christol. The description tak…
math.AC2004
Orbits of automorphism groups of fields
Kiran S. Kedlaya, Bjorn Poonen
We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has r…
math.AC2001
Algebraic Generalized Power Series and Automata
Kiran S. Kedlaya
A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. U…