Unambiguous Separators for Tropical Tree Automata
Séparateurs non-ambigus pour les automates tropicaux
Résumé
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.
Domaines
Logique en informatique [cs.LO]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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