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

Abstract

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Consider partial maps ∑* → 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.

How to cite

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Lombardy, 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 -

References

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