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Article . 2006
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Fundamenta Informaticae
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IOS PressPUB827Amsterdam, The Netherlands, The Netherlands/ undefined
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Abstract geometrical computation 1: embedding Black hole computations with rational numbers

descriptionPublicationkeyboard_double_arrow_right Article , Journal 01 Jan 2006 France English Publisher:IOS PressPUB827Amsterdam, The Netherlands, The NetherlandsJournal:Fundamenta Informaticae (issn: 0169-2968, Copyright policy )
Authors: Durand-Lose, Jérôme;

doi: 10.5555/2369467.2369473

Abstract geometrical computation 1: embedding Black hole computations with rational numbers

Abstract

The Black hole model of computation provides super-Turing computing power since it offers the possibility to decide in finite (observer's) time any recursively enumerable (r.e.) problem. In this paper, we provide a geometric model of computation, conservative abstract geometrical computation, that, although being based on rational numbers (and not real numbers), has the same property: it can simulate any Turing machine and can decide any r.e. problem through the creation of an accumulation. Finitely many signals can leave any accumulation, and it can be known whether anything leaves. This corresponds to a black hole effect.

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France
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Keywords

[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC], Black hole model, [INFO.INFO-CC] Computer Science/Computational Complexity, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Malament-Hogarth space-time, Zeno phenomena, [INFO.INFO-CG] Computer Science/Computational Geometry, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], [INFO.INFO-LO] Computer Science/Logic in Computer Science, [ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Energy conservation, Abstract geometrical computation, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [ INFO.INFO-CC ] Computer Science [cs]/Computational Complexity [cs.CC], [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], [INFO.INFO-DM] Computer Science/Discrete Mathematics, Super-Turing computation, [ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG], [ INFO.INFO-LO ] Computer Science [cs]/Logic in Computer Science [cs.LO], [INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC], Turing universality

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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