In this paper we show that Shannon's general purpose analog computer (GPAC) is equivalent to a particular class of recursive functions over the reals with the flavour of Kleene's classical recursive function theory.Expand

This paper revisits one of the first models of analog computation, the General Purpose Analog Computer (GPAC) and we show that it can be further refined.Expand

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine, as long as we are talking about bounded computations.Expand

In the last decade, the field of analog computation has experienced renewed interest. In particular, there have been several attempts to understand which relations exist between the many models of… Expand

We show that the realistic models of analog computation – namely the General Purpose Analog Computer (GPAC) – can simulate Turing machines in a computationally efficient manner.Expand