论文信息 - Stabilité Polynômiale des Corps Différentiels

Stabilité Polynômiale des Corps Différentiels

A notion of complexity for an arbitrary structure was defined in the book of Poizat Les petits cailloux (1995): we can define P and NP problems over a differential field K . Using the Witness Theorem of Blum et al., we prove the P -stability of the theory of differential fields: a P problem over a differential field K is still P when restricts to a sub-differential field k of K . As a consequence, if P = NP over some differentially closed field K , then P = NP over any differentially closed field and over any algebraically closed field.

Natacha Portier

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