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

Sylvain Lombardy; Jean Mairesse

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2006)

- 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 - Informatique Théorique et Applications 40.1 (2006): 1-14. <http://eudml.org/doc/245266>.

@article{Lombardy2006,

abstract = {Consider partial maps $\Sigma ^*$$\rightarrow $$\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 - Informatique Théorique et Applications},

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

language = {eng},

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/245266},

volume = {40},

year = {2006},

}

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 - Informatique Théorique et Applications

PY - 2006

PB - EDP-Sciences

VL - 40

IS - 1

SP - 1

EP - 14

AB - Consider partial maps $\Sigma ^*$$\rightarrow $$\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

UR - http://eudml.org/doc/245266

ER -

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