On the Computational Capabilities of Several Models

Bournez, Olivier; Hainry, Emmanuel

doi:10.1007/978-3-540-74593-8_2

Cited by 1 publication

(1 citation statement)

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“…Infinite computations also provide limits, for example computable analysis (Weihrauch, 2000, type-2 Turing machines) manipulates infinite inputs and generates infinite outputs, each one representing a real number. In analog computations, limit operators (as limits of sequences of real numbers) are also considered (Chadzelek and Hotz, 1999;Kawamura, 2005;Mycka, 2003bMycka, ,a, 2006Mycka and Costa, 2007;Bournez and Hainry, 2007).…”

Section: Introductionmentioning

confidence: 99%

Abstract geometrical computation 3: black holes for classical and analog computing

Durand-Lose

2009

Nat Comput

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geometrical computation 3: Black holes for classical and analog computingJérôme Durand-Lose To cite this version:Jérôme Durand-Lose. The date of receipt and acceptance will be inserted by the editorAbstract The so-called Black Hole model of computation involves a non Euclidean space-time where one device is infinitely "accelerated" on one world-line but can send some limited information to an observer working at "normal pace". The key stone is that after a finite duration, the observer has received the information or knows that no information was ever sent by the device which had an infinite time to complete its computation. This allows to decide semi-decidable problems and clearly falls out of classical computability.A setting in a continuous Euclidean space-time that mimics this is presented. Not only is Zeno effect possible but it is used to unleash the black hole power. Both discrete (classical) computation and analog computation (in the understanding of Blum, Shub and Smale) are considered. Moreover, using nested singularities (which are built), it is shown how to decide higher levels of the corresponding arithmetical hierarchies.Key words Abstract geometrical computation -Analog computationArithmetic hierarchy -Black hole model -Malament-Hogarth space-time -Hyper-computing -Zeno phenomenon Disclaimer The author is a computer scientist and not a physicist. So that it is refereed to other contributions in this issue and to the cited bibliography for enlightenment on black holes. The present article aims at providing a context of computation exhibiting the same computing capabilities as black holes and at illustrating the point of view of a computer scientist.

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Section: Introductionmentioning

confidence: 99%

Abstract geometrical computation 3: black holes for classical and analog computing

Durand-Lose

2009

Nat Comput

View full text Add to dashboard Cite

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On the Computational Capabilities of Several Models

Cited by 1 publication

References 15 publications

Abstract geometrical computation 3: black holes for classical and analog computing

Abstract geometrical computation 3: black holes for classical and analog computing

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