%0 Journal Article
%T On the computational complexity of algebraic numbers : the Hartmanis-Stearns problem revisited
%+ Institut Camille Jordan (ICJ)
%+ Combinatoire, théorie des nombres (CTN)
%+ Institut de Mathématiques de Marseille (I2M)
%+ Laboratoire d'Informatique et de Mathématiques (LIM)
%A Adamczewski, Boris
%A Cassaigne, Julien
%A Le Gonidec, Marion
%< avec comité de lecture
%@ 0002-9947
%J Transactions of the American Mathematical Society
%I American Mathematical Society
%N 373
%P 3085-3115
%8 2020
%D 2020
%R 10.1090/tran/7915
%K Hartmanis-Stearns problem
%K pushdown automata
%K transcendence
%K stack machines
%K integer base expansions
%K tag machines
%Z Mathematics [math]/Number Theory [math.NT]
%Z Mathematics [math]/Combinatorics [math.CO]
%Z Computer Science [cs]/Formal Languages and Automata Theory [cs.FL]Journal articles
%X — 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.
%G English
%2 https://hal.science/hal-01254293/document
%2 https://hal.science/hal-01254293/file/HartmanisStearns12%3A01%3A2016.pdf
%L hal-01254293
%U https://hal.science/hal-01254293
%~ UNIV-ST-ETIENNE
%~ AFRIQ
%~ CNRS
%~ ICJ
%~ UNIV-AMU
%~ UNIV-LYON1
%~ UNIV-REUNION
%~ INSA-LYON
%~ EC-LYON
%~ EC-MARSEILLE
%~ INSMI
%~ OPENAIRE
%~ LIM
%~ I2M
%~ I2M-2014-
%~ ICJ-CTN
%~ PAPANGUE
%~ INSA-GROUPE
%~ FST-REUNION
%~ UDL
%~ UNIV-LYON