Overlap-free morphisms and finite test-sets

Gwenaël Richomme (1) , Francis Wlazinski (1)

1 LaRIA - Laboratoire de Recherche en Informatique d'Amiens

We study finite test-sets for overlap-freeness of morphisms from a free monoid A* into another B*. When card(A) = card(B) = 2$, Berstel and Séébold have shown that such a finite test-set exists, and, Richomme and Séébold have characterized all of them. For other values of card(A) and card(B), we show whether or not exist such finite test-sets, and in the former case we characterize all of them. We also do this when considering uniform morphisms for all values of card(A) and card(B).

Mots clés: Combinatorics on words; overlap-free words; morphisms; test-sets

Domaines: Mathématique discrète [cs.DM]

Gwenaël Richomme, Francis Wlazinski. Overlap-free morphisms and finite test-sets. Discrete Applied Mathematics, 2004, 143 (1-3), pp.92-109. ⟨hal-00598221⟩