Computations over \(\mathbb{Z}\) and \(\mathbb{R}\): a comparison (Q923632)

This paper investigates the complexity classes over the real numbers. These classes are compared with the ordinary complexity classes (over \(\mathbb{Z})\). Because in the complexity classes over \(\mathbb{R}\) the basic computations with real numbers can be done in one step, the problems that are in the same complexity classes over \(\mathbb{Z}\) may be in different complexity classes over \(\mathbb{R}\) and vice versa.