2012
DOI: 10.1098/rsta.2011.0427
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Abstract: We developed earlier a theory of combining algorithms with physical systems, on the basis of using physical experiments as oracles to algorithms. Although our concepts and methods are general, each physical oracle requires its own analysis, on the basis of some fragment of physical theory that specifies the equipment and its behaviour. For specific examples of physical systems (mechanical, optical, electrical), the computational power has been characterized using non-uniform complexity classes. The powers of t… Show more

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Cited by 20 publications
(42 citation statements)
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“…We are finalising a paper (Beggs et al 2012a) that attempts to show just that; as our work on axiomatisations of physical oracles will demonstrate, the nature of the interface between experiment and Turing machine is surprisingly subtle. The first is how general are these results?…”
Section: Mathematics Versus Physicsmentioning
confidence: 94%
“…We are finalising a paper (Beggs et al 2012a) that attempts to show just that; as our work on axiomatisations of physical oracles will demonstrate, the nature of the interface between experiment and Turing machine is surprisingly subtle. The first is how general are these results?…”
Section: Mathematics Versus Physicsmentioning
confidence: 94%
“…Using the sound framework of Recursive Analysis, we assert the computability of a local strong solution of (1) in the space L σ 2,0 (Ω) (see Section 2 for definition) from a given initial condition a ∈ L σ 2,0 (Ω); moreover, the computation is uniform in the initial data. We follow a common strategy used in the classical existence proofs [3,4,5,18,21]: i) Eliminate the pressure P by applying, to both sides of Equation (1), the Helmholtz projection P : L 2 (Ω) 2 → L σ 2,0 (Ω), thus arriving at the nonlinear evolution equation…”
Section: Overviewmentioning
confidence: 99%
“…such that, for every a ∈ L σ 2,0 (Ω) and f ∈ C [0; ∞), L σ 2,0 (Ω) , the function (u, P ) : 0; T (a, f )] ∋ t → S(a, f , t) constitutes a (strong local in time and weak global in space) solution to Equation (1).…”
Section: Overviewmentioning
confidence: 99%
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“…-Beggs and co-workers [6] investigate an abstract framework for interfacing algorithms and physical systems, with the notion of oracle again taking centre stage. There are basic motivational questions to this work, including: 'How much information can be extracted from a physical process?…”
mentioning
confidence: 99%