Existence of finite test-sets for k-power-freeness of uniform morphisms
  A challenging problem is to find an algorithm to decide whether a morphism is k-power-free. We provide such an algorithm when k >= 3 for uniform morphisms showing that in such a case, contrarily to the general case, there exist finite test-sets for k-power-freeness. 
Gw\'ena\"el Richomme (LaRIA), Francis Wlazinski (LaRIA)