Victor Magron

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The aim of this work is to certify lower bounds for realvalued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales’ proof of Kepler’s conjecture yields thousands of(More)
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance, for FPGAs or custom hardware implementations. This problem becomes challenging when the program does not employ solely linear(More)
While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The verification of user-provided properties is not easily compatible with the usual forward fixpoint computation using(More)
Interpretation (VMCAI), volume 3385, pages 21–47, Paris,<lb>France, January 2005. Springer Verlag.<lb>[Ste74] Gilbert Stengle. A nullstellensatz and a positivstellensatz in semial-<lb>gebraic geometry. Mathematische Annalen, 207(2):87–97, 1974.<lb>[WKKM06] Hayato Waki, Sunyoung Kim, Masakazu Kojima, and Masakazu Mu-<lb>ramatsu. Sums of Squares and(More)
We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem minx∈S{(f1(x), f2(x))}, where f1 and f2 are two conflicting polynomial criteria and S ⊂ Rn is a compact basic semialgebraic set. We provide a systematic numerical scheme to approximate the Pareto curve. We start by reducing(More)