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

We study a restricted version of Shannon's general purpose analog computer in which we only allow the machine to solve linear differential equations.Expand

We consider whether the set G of GPAC-computable functions is closed under iteration, that is, whether for any function f(x)?G there is a function F(x, t)=ft(x) for nonnegative integers t.Expand

We discuss combining physical experiments with machine computations and introduce a form of analogue–digital (AD) Turing machine that can compute more than classical Turing machines.Expand

The theory of analog computation, where the internal states of a computer are continuous rather than discrete, has enjoyed a recent resurgence of interest.Expand

We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the… Expand