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Abstract(s)
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
Description
Keywords
Analog computation recursion theory computable functions universal computation
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Publisher
Department of Informatics, University of Lisbon