  We consider the complexity of integer base expansions of algebraic irrational
numbers from a computational point of view. We show that the Hartmanis--Stearns
problem can be solved in a satisfactory way for the class of multistack
machines. In this direction, our main result is that the base-$b$ expansion of
an algebraic irrational real number cannot be generated by a deterministic
pushdown automaton. We also confirm an old claim of Cobham proving that such
numbers cannot be generated by a tag machine with dilation factor larger than
one.
