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On the computational complexity of algebraic numbers : the Hartmanis-Stearns problem revisited

Abstract : — 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.
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Contributor : Boris Adamczewski <>
Submitted on : Tuesday, January 12, 2016 - 2:40:01 PM
Last modification on : Wednesday, June 30, 2021 - 9:40:07 PM
Long-term archiving on: : Thursday, November 10, 2016 - 11:40:25 PM

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Boris Adamczewski, Julien Cassaigne, Marion Le Gonidec. On the computational complexity of algebraic numbers : the Hartmanis-Stearns problem revisited. Transactions of the American Mathematical Society, American Mathematical Society, 2020, pp.3085-3115. ⟨10.1090/tran/7915⟩. ⟨hal-01254293⟩

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