On the computational complexity of algebraic numbers: the   Hartmanis--Stearns problem revisited
  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. 
Boris Adamczewski, Julien Cassaigne, and Marion Le Gonidec
math.NT cs.CC math.CO