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Algebraic Generalized Power Series and Automata

Kiran S. Kedlaya
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Abstract

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. Using Christol's result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).

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Kiran S. Kedlaya. 2001-10-08. Algebraic Generalized Power Series and Automata. https://arxiv.org/abs/math/0110089

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