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The Extended Analog Computer and Functions Computable in a Digital Sense
Abstract (in LaTeX format)
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 $\mathbb{N}$. 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.
Kewords: analog computation, Extended Analog Computer, recursion theory, recursive functions.
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BibTeX entry
@article{Piekarz:2010:ActaCybernetica,author = {Monika Piekarz},
title = {The Extended Analog Computer and Functions Computable in a Digital Sense},
journal = {Acta Cybernetica},
volume = {19},
number= {4},
pages = {749--764},
year = {2010},
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 $\mathbb{N}$. 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.},
keywords = {analog computation, Extended Analog Computer, recursion theory, recursive functions}
}