Hypercomputation or super-Turing computation refers to models of computation that go beyond, or are incomparable to, Turing computability. This includes various hypothetical methods for the computation of non-Turing-computable functions, following super-recursive algorithms (see also supertask). The term "super-Turing computation" appeared in a 1995 Science paper by Hava Siegelmann. The term "hypercomputation" was introduced in 1999 by Jack Copeland and Diane Proudfoot.
The terms are not quite synonymous: "super-Turing computation" usually implies that the proposed model is supposed to be physically realizable, while "hypercomputation" does not.
Technical arguments against the physical realizability of hypercomputations have been presented.
Read more about Hypercomputation: History, Hypercomputation and The Church–Turing Thesis, Hypercomputer Proposals, Analysis of Capabilities, Taxonomy of "super-recursive" Computation Methodologies, Criticism