[Todos CMAT] Conferencia de Raffalli (Cmat)
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Lun Mar 3 21:59:54 UYST 2014
Title: Hilbert's 17th problem via cut-elimination
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
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