  The elementary affine lambda-calculus was introduced as a polyvalent setting
for implicit computational complexity, allowing for characterizations of
polynomial time and hyperexponential time predicates. But these results rely on
type fixpoints (a.k.a. recursive types), and it was unknown whether this
feature of the type system was really necessary. We give a positive answer by
showing that without type fixpoints, we get a characterization of regular
languages instead of polynomial time. The proof uses the semantic evaluation
method. We also propose an aesthetic improvement on the characterization of the
function classes FP and k-FEXPTIME in the presence of recursive types.
