Author(s): Campagnolo, Manuel Lameiras ; Moore, Cristopher ; Costa, José Félix
Date: 1998
Persistent ID: http://hdl.handle.net/10451/14111
Origin: Repositório da Universidade de Lisboa
Subject(s): Analog computation; recursion theory; computable functions; universal computation
In this paper we extend the class of differentially algebraic functions computed by Shannon's General Purpose Analog Computer (GPAC). We relax Pour-El's definition of GPAC to obtain new operators and we use recursion theory on the reals to define a new class of analog computable functions. We show that a function F(t,x) which simulates t time-steps of a Turing machine on input x, and more generally a functional that allows us to define the t'th iterate of a definable function, are definable in this system. Therefore, functions like Gamma which are not generable by GPAC become computable in this extension
