On a Transfer Theorem for the P\ne NP conjecture
Gregorio Malajovich
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 $\mathcal P \ne \mathcal {NP}$ Conjecture is proved, namely: $\mathcal P \ne \mathcal {NP}$ in this model over the real algebraic numbers if and only if $\mathcal P \ne \mathcal {NP}$ in the classical setting.