The extended analog computer and functions computable in a digital sense

Abstract

In this paper we compare the computational power of the Extended Analog Computer (EAC) with partial recursive functions. We first give a survey of some part of computational theory in discrete and in real space. In the last section we show that the EAC can generate any partial recursive function defined over N. Moreover we conclude that the classical halting problem for partial recursive functions is an equivalent of testing by EAC if sets are empty or not.