Series which are both max-plus and min-plus rational are unambiguous
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 1, p. 1-14

Consider partial maps ${\Sigma }^{*}$ $\to$ $ℝ$ 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.

DOI : https://doi.org/10.1051/ita:2005042
Classification:  68Q19,  68Q45,  68Q70
Keywords: rational series, automata, unambiguous, max-plus semiring, tropical semiring
@article{ITA_2006__40_1_1_0,
author = {Lombardy, Sylvain and Mairesse, Jean},
title = {Series which are both max-plus and min-plus rational are unambiguous},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
publisher = {EDP-Sciences},
volume = {40},
number = {1},
year = {2006},
pages = {1-14},
doi = {10.1051/ita:2005042},
zbl = {1085.68081},
mrnumber = {2197280},
language = {en},
url = {http://www.numdam.org/item/ITA_2006__40_1_1_0}
}

Lombardy, Sylvain; Mairesse, Jean. Series which are both max-plus and min-plus rational are unambiguous. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 1, pp. 1-14. doi : 10.1051/ita:2005042. http://www.numdam.org/item/ITA_2006__40_1_1_0/

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