Algebraic Generalized Power Series and Automata
Kiran S. Kedlaya · arXiv (Cornell University) · 2001
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).