[Todos CMAT] Conferencia de Raffalli (Cmat)
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Lun Mar 3 22:23:18 UYST 2014
Title: Hilbert's 17th problem via cut-elimination
> Christophe Raffalli
> Univ. de Savoie
> Sala de Conferencias del Piso 15
> Miercoles 5 de marzo, 11horas
> Abstract: Hilbert's seventeen problem, solved by Artin, says that
> every positive polynomial can be written as a sum of squares of
> rational fraction. Since Artin, effective proof have been given by
> Lombardi - Roy - Perrucci for the latest one which give a bound to the
> degree as a tower of five exponentials.
> We will see how such a proof can be presented as a result of cut
> elimination, showing that replacing model theory by proof theory is a
> possible method to make a result effective.
> The main contribution of our work is the fact that we implemented the
> procedure and we introduced a notion of PBDD that requires smaller
> degrees, making it possible to extract the wanted equalities yet only for
> simplest positive polynomials (which was not possible before from such an
> effective proof).
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