Series which are both max-plus and min-plus rational are unambiguous

Sylvain Lombardy (1) , Jean Mairesse (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

Consider partial maps from the free monoid into the field of real numbers with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one that recognize the same series.

Mots clés: rational series; automata; unambiguous; max-plus semiring; tropical semiring

Domaines: Mathématique discrète [cs.DM]

Sylvain Lombardy, Jean Mairesse. Series which are both max-plus and min-plus rational are unambiguous. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2006, 40, pp.1-14. ⟨10.1051/ita:2005042⟩. ⟨hal-00017220⟩