Real computation

Within this theory, it is possible to prove interesting statements such as "The complement of the Mandelbrot set is only partially decidable."

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.)

(Claude Shannon's idealized analog computer can only solve algebraic differential equations, while a digital computer can solve some transcendental equations as well.

)[2] A canonical model of computation over the reals is Blum–Shub–Smale machine (BSS).

Unlimited precision real numbers in the physical universe are prohibited by the holographic principle and the Bekenstein bound.

Circuit diagram of an analog computing element to integrate a given function. Real computation theory investigates properties of such devices under the idealizing assumption of infinite precision.