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Theses

Réduction du nombre de variables en analyse de relations linéaires

Abstract : This thesis takes place in automatic verification of numerical
properties, mainly for embeded softwares. During verification one
must represents in a finished way possibly infinite sets of values,
for that a solution is use of convex polyhedra. This representation
is precise but expensive so maximal number of variables is limited.
The goal of this thesis is to increase the maximum number of variables
which it is possible to represent. Two approaches were considered then
tested. First we wanted to benefit from the presence of linear equations
to eliminate a variable by equation. This approach appeared, in
experiments, rather disappointing. Another apprroach, more promising, is
the use of cartesian product. The idea is then to represent
independently the variables whose evolution is not dependent. This
decomposition can be improved through a change of basis. An analyser was
done in order to test these two approaches.
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Theses
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https://tel.archives-ouvertes.fr/tel-00012143
Contributor : David Merchat <>
Submitted on : Thursday, April 13, 2006 - 8:02:37 PM
Last modification on : Thursday, November 19, 2020 - 3:58:02 PM
Long-term archiving on: : Saturday, April 3, 2010 - 10:17:52 PM

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David Merchat. Réduction du nombre de variables en analyse de relations linéaires. Autre [cs.OH]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00012143⟩

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