| Issue |
RAIRO-Theor. Inf. Appl.
Volume 40, Number 1, January-March 2006
|
|
|---|---|---|
| Page(s) | 1 - 14 | |
| DOI | https://doi.org/10.1051/ita:2005042 | |
| Published online | 15 October 2005 | |
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;
lombardy@liafa.jussieu.fr, mairesse@liafa.jussieu.fr
Received:
June
2004
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.
© EDP Sciences, 2006
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