id: 05008971
dt: j
an: 05008971
au: Lombardy, Sylvain; Mairesse, Jean
ti: Series which are both max-plus and min-plus rational are unambiguous.
so: Theor. Inform. Appl. 40, No. 1, 1-14 (2006).
py: 2006
pu: EDP Sciences, Les Ulis
la: EN
cc: 
ut: rational series; automata; unambiguous; max-plus semiring; tropical
    semiring
ci: 
li: doi:10.1051/ita:2005042 numdam:ITA_2006__40_1_1_0
ab: Summary: Consider partial maps $Σ^*\to {\bbfR}$ 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.
rv: