Algebraic Elimination of epsilon-transitions
  We present here algebraic formulas associating a k-automaton to a k-epsilon-automaton. The existence depends on the definition of the star of matrices and of elements in the semiring k. For this reason, we present the theorem which allows the transformation of k-epsilon-automata into k-automata. The two automata have the same behaviour. 
Gerard Duchamp (LIFAR, LIPN), Hatem Hadj Kacem (LIFAR), Eric   Laugerotte (LIFAR)