Titlebook: Computation, Physics and Beyond; International Worksh Michael J. Dinneen,Bakhadyr Khoussainov,André Nies Book 2012 Springer-Verlag GmbH Ber

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Fundamentals of Topological Insulators,mputable functions, the existence of universal machines and the invariance under the choice of machine. Recently, the notion of descriptional complexity for finite-state computable functions has been introduced by Calude et al. For the latter theory, one cannot rely on the existence of universal mac

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https://doi.org/10.1007/978-3-658-11811-2d in classical language, yield major algorithmic randomness notions. He proved several results connecting constructive analysis and randomness that were rediscovered only much later..We give an overview in mostly chronological order. We sketch a proof that Demuth’s notion of Denjoy sets (or reals) c

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Dynamic correlations in quantum magnets, a first order formula on the integers and decides (after a finite number of computations and always with a right answer) whether this formula is true or false. There are also many other limitations of usual computing theory that can be seen as generalisations of Gödel incompleteness theorem: for ex

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Luttinger liquids: the basic concepts,ere a computable bound on the use function is explicitly specified. This elaboration enables us to deal with the notion of asymptotic behavior in a manner like in computational complexity theory, while staying in computability theory. We apply the elaboration to sets which appear in the statistical

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Computation, Physics and Beyond978-3-642-27654-5Series ISSN 0302-9743 Series E-ISSN 1611-3349

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