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- Real_computation abstract "In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as \"The complement of the Mandelbrot set is only partially decidable.\"These hypothetical computing machines can be viewed as idealised analog computers which operate on real numbers, whereas digital computers are limited to computable numbers. They may be further subdivided into differential and algebraic models (digital computers, in this context, should be thought of as topological, at least insofar as their operation on computable reals is concerned). Depending on the model chosen, this may enable real computers to solve problems that are inextricable on digital computers (For example, Hava Siegelmann's neural nets can have noncomputable real weights, making them able to compute nonrecursive languages.) or vice versa. (Claude Shannon's idealized analog computer can only solve algebraic differential equations, while a digital computer can solve some transcendental equations as well. However this comparison is not entirely fair since in Claude Shannon's idealized analog computer computations are immediately done; i.e. computation is done in real time. Shannon's model can be adapted to cope with this problem.)A canonical model of computation over the reals is Blum–Shub–Smale machine (BSS).If real computation were physically realizable, one could use it to solve NP-complete problems, and even #P-complete problems, in polynomial time. Unlimited precision real numbers in the physical universe are prohibited by the holographic principle and the Bekenstein bound.".
- Real_computation wikiPageExternalLink lsm-telematik.pdf.
- Real_computation wikiPageID "397247".
- Real_computation wikiPageLength "3715".
- Real_computation wikiPageOutDegree "26".
- Real_computation wikiPageRevisionID "646983661".
- Real_computation wikiPageWikiLink Algebra.
- Real_computation wikiPageWikiLink Analog_computer.
- Real_computation wikiPageWikiLink Artificial_neural_network.
- Real_computation wikiPageWikiLink Bekenstein_bound.
- Real_computation wikiPageWikiLink Blum–Shub–Smale_machine.
- Real_computation wikiPageWikiLink Category:Hypercomputation.
- Real_computation wikiPageWikiLink Category:Theory_of_computation.
- Real_computation wikiPageWikiLink Claude_Shannon.
- Real_computation wikiPageWikiLink Computability.
- Real_computation wikiPageWikiLink Computability_theory.
- Real_computation wikiPageWikiLink Computable_number.
- Real_computation wikiPageWikiLink Computer.
- Real_computation wikiPageWikiLink Differential_(mathematics).
- Real_computation wikiPageWikiLink Hava_Siegelmann.
- Real_computation wikiPageWikiLink Holographic_principle.
- Real_computation wikiPageWikiLink Hypercomputation.
- Real_computation wikiPageWikiLink Lenore_Blum.
- Real_computation wikiPageWikiLink Mandelbrot_set.
- Real_computation wikiPageWikiLink NP-completeness.
- Real_computation wikiPageWikiLink Real_number.
- Real_computation wikiPageWikiLink Sharp-P.
- Real_computation wikiPageWikiLink Stephen_Smale.
- Real_computation wikiPageWikiLink Time_complexity.
- Real_computation wikiPageWikiLink Topology.
- Real_computation wikiPageWikiLinkText "Real computation".
- Real_computation wikiPageWikiLinkText "real computation".
- Real_computation wikiPageWikiLinkText "real computer".
- Real_computation wikiPageWikiLinkText "real numbers".
- Real_computation wikiPageUsesTemplate Template:Cite_book.
- Real_computation wikiPageUsesTemplate Template:Comp-sci-stub.
- Real_computation subject Category:Hypercomputation.
- Real_computation subject Category:Theory_of_computation.
- Real_computation type Area.
- Real_computation type Area.
- Real_computation comment "In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers.".
- Real_computation label "Real computation".
- Real_computation sameAs Q7301125.
- Real_computation sameAs Computação_real.
- Real_computation sameAs m.023fy0.
- Real_computation sameAs Q7301125.
- Real_computation wasDerivedFrom Real_computation?oldid=646983661.
- Real_computation isPrimaryTopicOf Real_computation.