Diophantine equations in characteristic p and finite automata

Abstract
I will explain how the theory of finite automata can be relevant to describe the solutions of some Diophantine equations defined over fields of characteristic p. This approach applies in particular to the Skolem-Mahler-Lech theorem, the S-unit equation, and some case of the Mordell-Lang Theorem. An especially interesting feature of the method is that it leads to effective results. This is a joint work with Jason Bell.