Derived terms without derivation a shifted perspective on the derived-term automaton - Lombardy, Sylvain; Sakarovitch, Jacques (Journal of Computer Science and Cybernetics, 2021)
We present here a construction for the derived term automaton (aka partial derivative, or Antimirov, automaton) of a rational (or regular) expression based on a sole induction on the depth of the expression and without making reference to an operation of derivation of the expression. It is particularly well-suited to the case of weighted rational expressions.