On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited
Number Theory
2017-11-15 v2 Computational Complexity
Combinatorics
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- 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.
Keywords
Cite
@article{arxiv.1601.02771,
title = {On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited},
author = {Boris Adamczewski and Julien Cassaigne and Marion Le Gonidec},
journal= {arXiv preprint arXiv:1601.02771},
year = {2017}
}