Real Number Computations: On the Use of Information

AbstractWhen comparing complexity theory over the ring Z (Turing machine) on one hand and over the ring R (Blum-Shub-Smale machine) on the other hand, it will be important to study how methods and ideas of the first can be transformed to the second one. In this sense the present paper is concerned with the relation between a characterization of the P = NP?-question for the Z-case (given by Krentel) and a special class of quadratic-programming problems which are important in the real model