Overlap-free morphisms and finite test-sets Original Research Article

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).