Derived Terms without Derivation -- A shifted perspective on the derived-term automaton

Sylvain Lombardy (1, 2) , Jacques Sakarovitch (3, 4, 5)

1 Bordeaux INP - Institut Polytechnique de Bordeaux
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 CNRS - Centre National de la Recherche Scientifique
4 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
5 Télécom Paris

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.

Domaines: Théorie et langage formel [cs.FL]

Sylvain Lombardy, Jacques Sakarovitch. Derived Terms without Derivation -- A shifted perspective on the derived-term automaton. Journal of Computer Science and Cybernetics, Vietnamese Academy of Science and Technology, Vietnam, 2021, 37 (3), pp.201-221. ⟨10.15625/1813-9663/37/3/16263⟩. ⟨hal-03382261⟩