Comparaison approchée des fonctions calculées par automates min-plus
Laure Daviaud
LIF, Aix-Marseille Université
https://www.city.ac.uk/about/people/academics/laure-daviaud
Date(s) : 20/01/2015 iCal
11h05 - 12h00
Approximate comparison of functions calculated by min-plus automata
The min-plus automata are weighted automata on the semiring $(NU \{+\ infty\}, min,+) $ which compute functions of the set of words (on a finite alphabet) in $NU \{+\ infty\}$. The problem of testing whether $f<g$ for two such functions is an undecidable problem (Krob, 92). Nevertheless, we will see that an approximation of this problem becomes decidable: there exists an algorithm which, given $e>0$ and two functions f and g calculated by min-plus automata, answers « yes » if $f<g$, « no » if there exists a word w such as $f (w)>(1+e)g(w)$, and indifferently « yes » or « no » in the other cases. The proof of this result joins l study of finely generated tropical matrix semi-groups, for which we give an approximation of the upper envelope. This work is a joint work with Thomas Colcombet (LIAFA).
https://hal.archives-ouvertes.fr/hal-00712771/
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