On a transfer theorem for the P not equal NP conjecture
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 not equal NP Conjecture is proved, namely: P not equal NP in this model over the real algebraic numbers if and only if P not equal NP in the classical setting. (C) 2001 Academic Press.
transfer theorem height np-completeness computability over a ring