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

Sylvain Lombardy; Jean Mairesse

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 40, Issue: 1, page 1-14
- ISSN: 0988-3754

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topLombardy, Sylvain, and Mairesse, Jean. "Series which are both max-plus and min-plus rational are unambiguous." RAIRO - Theoretical Informatics and Applications 40.1 (2010): 1-14. <http://eudml.org/doc/92787>.

@article{Lombardy2010,

abstract = {
Consider partial maps ∑* → $\mathbb R$ 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.
},

author = {Lombardy, Sylvain, Mairesse, Jean},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Rational series; automata; unambiguous; max-plus semiring;
tropical semiring.; rational series; tropical semiring},

language = {eng},

month = {3},

number = {1},

pages = {1-14},

publisher = {EDP Sciences},

title = {Series which are both max-plus and min-plus rational are unambiguous},

url = {http://eudml.org/doc/92787},

volume = {40},

year = {2010},

}

TY - JOUR

AU - Lombardy, Sylvain

AU - Mairesse, Jean

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

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 40

IS - 1

SP - 1

EP - 14

AB -
Consider partial maps ∑* → $\mathbb R$ 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.

LA - eng

KW - Rational series; automata; unambiguous; max-plus semiring;
tropical semiring.; rational series; tropical semiring

UR - http://eudml.org/doc/92787

ER -

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