Direct and dual laws for automata with multiplicities
  We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities in several noncommutative variables). We show that classical formulas are ``almost every time'' optimal, characterize the dual laws preserving rationality and also relators that are compatible with these laws. 
G\'erard Duchamp (LIPN), Marianne Flouret (LIH EA3219), Eric   Laugerotte (LIFAR EA2655), Jean-Gabriel Luque (IGM-LabInfo)