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

Published online by Cambridge University Press:  15 October 2005

Sylvain Lombardy  and
Jean Mairesse
Sylvain Lombardy
Affiliation:
LIAFA (UMR 7089), CNRS–Université Paris 7, 2 pl. Jussieu, 75251 Paris Cedex 05, France; [email protected], [email protected]
Jean Mairesse
Affiliation:
LIAFA (UMR 7089), CNRS–Université Paris 7, 2 pl. Jussieu, 75251 Paris Cedex 05, France; [email protected], [email protected]
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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.

Keywords

Rational seriesautomataunambiguousmax-plus semiringtropical semiring.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 1 , January 2006 , pp. 1 - 14
Copyright
© EDP Sciences, 2006

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