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Analog computers and recursive functions over the reals
TLDR
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
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Some recent developments on Shannon's General Purpose Analog Computer
TLDR
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
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Turing Machines Can Be Efficiently Simulated by the General Purpose Analog Computer
TLDR
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
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Polynomial dierential equations compute all real computable functions
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 ofExpand
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Computability via analog circuits
TLDR
In this paper we are interested in a particular model of analog computation, the General Purpose Analog Computer (GPAC). Expand
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Analog models of computations \& Effective Church Turing Thesis: Efficient simulation of Turing machines by the General Purpose Analog Computer
TLDR
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