- Real computation
In

computability theory , the theory of**real computation**deals with hypothetical computing machines using infinite-precisionreal number s. They are given this name because they operate on the set ofreal number s. Within this theory, it is possible to prove interesting statements such as "the complement of theMandelbrot set is only partially decidable". For other such powerful machines, see the articleHypercomputation .These hypothetical computing machines can be viewed as idealised

analog computer s which operate on real numbers and are differential, whereasdigital computer s are limited tocomputable numbers and arealgebraic . Depending on the model chosen, this may enable real computers to solve problems that are inextricable on digital computers (for example,Hava Siegelmann 'sneural 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).A canonical model of computation over the reals is

Blum Shub Smale machine (BSS).**Further reading***

Lenore Blum ,Felipe Cucker ,Michael Shub andStephen Smale , "Complexity and Real Computation", ISBN 0387982817.**External links*** "Neural Networks and Analog Computation: Beyond the Turing Limit" by

Hava Siegelmann ISBN 0-8176-3949-7

* [*http://www.lsm.tugraz.at/papers/lsm-telematik.pdf the Liquid Computer A Novel Strategy for Real-Time Computing on Time Series, by Thomas Natschläger et al*]

* [ftp://ftp.cs.cuhk.hk/pub/neuro/papers/jcss1.ps.Z On the computational power of neural nets]

* [*http://math.isa.utl.pt/~mlc/phdthesis.ps Computational complexity of real valued recursive functions and analog circuits. by Campagnolo*]

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