Unambiguous Separators for Tropical Tree Automata

Séparateurs non-ambigus pour les automates tropicaux

Thomas Colcombet (1, 2) , Sylvain Lombardy (3)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 CNRS - Centre National de la Recherche Scientifique
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function f and a min-plus automaton (similar) computing a function g such that f ⩽ g, there exists effectively an unambiguous tropical automaton computing h such that f ⩽ h ⩽ g. This generalizes a result of Lombardy and Mairesse of 2006 stating that series which are both max-plus and min-plus rational are unambiguous. This generalization goes in two directions: trees are considered instead of words, and separation is established instead of characterization (separation implies characterization). The techniques in the two proofs are very different.

Mots clés: Tree automata; Tropical semiring; Separation; Unambiguity

Domaines: Logique en informatique [cs.LO]

Thomas Colcombet, Sylvain Lombardy. Unambiguous Separators for Tropical Tree Automata. 37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020, Mar 2020, Montpellier, France. pp.32:1-32:13, ⟨10.4230/LIPIcs.STACS.2020.32⟩. ⟨hal-03106897⟩