Abstract

In this paper we deal with the logical description of complexity classes arising in the real number model of computation introduced by Blum, Shub, and Smale [4]. We adapt the approach of descriptive complexity theory for this model developped in [14] and extend it to capture some further complexity classes over the reals by logical means. Among the latter we find NC$_\mathbb{R}$, PAR$_\mathbb{R}$, EXP$_\mathbb{R}$ and some others more.