On a Transfer Theorem for the P != NP Conjecture

Abstract 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 P ≠ N P Conjecture is proved, namely: P ≠ N P in this model over the real algebraic numbers if and only if P ≠ N P in the classical setting.

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