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

Consider partial maps Σ∗ −→   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. R´esum´e On consid`ere les fonctions de Σ∗ dans   `a domaine rationnel. On montre que deux familles remarquables de telles s´eries co¨ıncident: d’une part, les s´eries rationnelles non ambigu¨es, et d’autre part les s´eries qui sont `a la fois max-plus et min-plus rationnelles. Cel permet d’unifier les rsultats de d´ecidabilit´e de l’´egalit´e de deux s´eries, qui avaient ´et´e montr´es ind´ependament pour chacune de ces deux familles. On donne un algorithme ...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Sylvain Lombardy, Jean Mairesse
• Keywords: CORR 2007, Education, Min-plus Rational Series, Rational Series, Unambiguous Rational Series