[Todos CMAT] Conferencia de Raffalli (Cmat)

Walter Ferrer wrferrer en gmail.com
Lun Mar 3 21:59:54 UYST 2014

Title: Hilbert's 17th problem via cut-elimination
Christophe Raffalli
Univ. de Savoie
Sala de Conferencias del Piso 15

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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