A new proof for the decidability of D0L ultimate periodicity

We give a new proof for the decidability of the D0L ultimate periodicity problem based on the decidability of p-periodicity of morphic words adapted to the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F_2) of automorphisms of the rank two free group F_2 and show that it can be realized as a monoid in the group B_4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F_2 lifting any given basis of the free abelian group Z^2. We further give an algorithm allowing to decide whether two elements of F_2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure

Characterization of Test-Sets for Overlap-Free Morphisms

We give a characterization of all the sets X such that any morphism h on fa; bg is overlap-free iff for all x in X, h(x) is overlap-free. As a consequence, we observe the particular case X = fbbabaag which improves the previous characterization of Berstel-Séébold [2]