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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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Object Specification Logic
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An Analog Characterization of the Grzegorczyk Hierarchy
TLDR
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
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Iteration, Inequalities, and Differentiability in Analog Computers
TLDR
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
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Computational complexity with experiments as oracles
TLDR
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
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Oracles that measure thresholds: the Turing machine and the broken balance
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What Lies Beyond the Mountains?
TLDR
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
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Mirror, Mirror in my Hand: A Duality between Specifications and Models of Process Behaviour
TLDR
We show that, besides its expressive power, Temporal Logic enjoys a very strong structural property: it is categorical on processes. Expand
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The P ne NP conjecture in the context of real and complex analysis
TLDR
In this paper, we aim at an analog characterization of the classical P ≠ NP conjecture of Structural Complexity. Expand
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Limits to measurement in experiments governed by algorithms
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 theExpand
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