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Hypercomputation is the theory of methods for the computation of non-recursive functions. The classes of functions which they can compute is studied in the field known as recursion theory. A similar recent term is super-Turing computation, which has been used in the neural network literature to describe machines with various expanded abilities, including the ability to compute directly on real numbers, the ability to carry out infinitely many computations simultaneously, or the ability to carry out computations with exponentially lower complexity than standard Turing machines.

Hypercomputation was first introduced by Alan Turing in his 1939 paper Systems of logic based on ordinals, which investigated mathematical systems in which an oracle was available to compute a single arbitrary (non-recursive) function from naturalss to naturals.

Other posited kinds of hypercomputer include:

At this stage, none of these devices seem physically plausible, and so hypercomputers are likely to remain a mathematical fiction.

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1 See also

See also


  1. There have been some claims to this effect; see Tien Kieu, Quantum Algorithm for Hilbert's Tenth Problem and the ensuing literature. It is very likely that these results will turn out to be erroneous or non-physical. Until this is well established and explained, the possibility of quantum hypercomputation is deserving of investigation.


  1. Alan Turing, Systems of logic based on ordinals, Proc. London math. soc., 45, 1939
  2. Tien Kieu, Quantum Algorithm for the Hilbert's Tenth Problem, Int. J. Theor. Phys., 42 (2003) 1461-1478, e-print archive quant-ph/0110136 (pdf format)
  3. Toby Ord, Hypercomputation: computing more than the Turing machine (pdf format), Honours Thesis, University of Melbourne, 2002.