Editing Hypercomputation (section)

{{Short description|Models of computation}}
'''Hypercomputation''' or '''super-Turing computation''' is a set of hypothetical [[model of computation|models of computation]] that can provide outputs that are not [[Turing-computable]]. For example, a machine that could solve the [[halting problem]] would be a hypercomputer; so too would one that could [[Entscheidungsproblem|correctly evaluate every statement]] in [[Peano arithmetic]].

The [[Church–Turing thesis]] states that any "computable" function that can be computed by a mathematician with a pen and paper using a finite set of simple algorithms, can be computed by a Turing machine. Hypercomputers compute functions that a [[Turing machine]] cannot and which are, hence, not computable in the Church–Turing sense.

Technically, the output of a [[random Turing machine]] is uncomputable; however, most hypercomputing literature focuses instead on the [[computation]] of deterministic, rather than random, uncomputable functions.