# Is Hartmanis-Stearns conjecture settled by this article?

The paper

"On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited"
by Boris Adamczewski, Julien Cassaigne, Marion Le Gonidec
https://arxiv.org/abs/1601.02771

claims in Theorem 2.3: " An algebraic irrational real number cannot be generated by a one-stack machine, or equivalently, by a determistic push down automaton."

I have read and checked the article, have not found any gap in it, and thus the Hartmanis-Stearns conjecture is closed by the theorem? Since the conjecture is hard to prove, I suspect that I misunderstood the article or some fault in it.

• But the Hartmanis-Stearn conjecture is about computability by a real Turing machine, not just by a (D)PDA. This paper proves a weaker form. – Lamine Sep 18 '17 at 10:35