Series which are both max-plus and min-plus rational are unambiguous
LIAFA (UMR 7089), CNRS–Université Paris 7,
2 pl. Jussieu, 75251 Paris Cedex 05, France;
Accepted: November 2004
Consider partial maps ∑* → 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.
Mathematics Subject Classification: 68Q19 / 68Q45 / 68Q70
Key words: Rational series / automata / unambiguous / max-plus semiring / tropical semiring.
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