It is observed that Derksen’s Skolem–Mahler–Lech theorem is a special case of the isotrivial positive characteristic Mordell-Lang theorem due to the second author and Scanlon. This motivates an extension of the classical notion of a $k$-automatic subset of the natural numbers to that of an $F$-automatic subset of a finitely generated abelian group $\Gamma $ equipped with an endomorphism $F$. Applied to the Mordell–Lang context, where $F$ is the Frobenius action on a commutative algebraic group $G$ over a finite field, and $\Gamma $ is a finitely generated $F$-invariant subgroup of $G$, it is shown that the “$F$-subsets” of $\Gamma $ introduced by the second author and Scanlon are $F$-automatic. It follows that when $G$ is semiabelian and $X\subseteq G$ is a closed subvariety then $X\cap... \Gamma $ is $F$-automatic. Derksen’s notion of a $k$-normal subset of the natural numbers is also here extended to the above abstract setting, and it is shown that $F$-subsets are $F$-normal. In particular, the $X\cap \Gamma $ appearing in the Mordell-Lang problem are $F$-normal. This generalises Derksen’s Skolem–Mahler–Lech theorem to the Mordell–Lang context.