On a Transfer Theorem for the P\ne NP conjecture

Gregorio Malajovich

\def\pnp{$\mathcal P \ne \mathcal {NP}$}

A model of computation is defined over the algebraic numbers and over number fields. This model is non-uniform, and the cost of operations depends on the height of the operands and on the degree of the extension of the rational defined by those operands.

A transfer theorem for the \pnp Conjecture is proved, namely: \pnp in this model over the real algebraic numbers if and only if \pnp in the classical setting.