超计算
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超计算或超图灵计算可以输出非图灵可计算结果的计算模型。例如，一台可以解决停机问题的机器可算作一台超计算机；可以正确推演皮亚诺算术中每一个状态的机器亦然。
邱奇－图灵论题指出，任何可以用有限算法以纸笔计算的"可有效计算"函数都能被图灵机计算。超计算机能计算图灵机无法计算、即邱奇－图灵论题中不可计算的的函数。
严格说来概率图灵机的输出是不可计算的。然而，大多数超计算方向的文献更关注有用的计算而非随机、不可计算的函数。
扩展阅读
- Mario Antoine Aoun, "Advances in Three Hypercomputation Models （页面存档备份，存于互联网档案馆）", (2016)
- L. Blum, F. Cucker, M. Shub, S. Smale, Complexity and Real Computation, Springer-Verlag 1997. General development of complexity theory for abstract machines that compute on real numbers instead of bits.
- Burgin, M. S. (1983) Inductive Turing Machines, Notices of the Academy of Sciences of the USSR, v. 270, No. 6, pp. 1289–1293
- Keith Douglas. Super-Turing Computation: a Case Study Analysis （页面存档备份，存于互联网档案馆） (PDF), M.S. Thesis, Carnegie Mellon University, 2003.
- Mark Burgin (2005), Super-recursive algorithms, Monographs in computer science, Springer. ISBN 0-387-95569-0
- Cockshott, P. and Michaelson, G. Are there new Models of Computation? Reply to Wegner and Eberbach, The computer Journal, 2007
- Cooper, S. B. Definability as hypercomputational effect (PDF). Applied Mathematics and Computation. 2006, 178: 72–82 [2017-12-20]. doi:10.1016/j.amc.2005.09.072. （原始内容 (PDF)存档于2011-07-24）.
- Cooper, S. B.; Odifreddi, P. Incomputability in Nature. S. B. Cooper and S. S. Goncharov (编). Computability and Models: Perspectives East and West (PDF). Plenum Publishers, New York, Boston, Dordrecht, London, Moscow. 2003: 137–160 [2017-12-20]. （原始内容 (PDF)存档于2011-07-24）.
- Copeland, J. (2002) Hypercomputation, Minds and machines, v. 12, pp. 461–502
- Davis, Martin (2006), "The Church–Turing Thesis: Consensus and opposition". Proceedings, Computability in Europe 2006. The requested URL /~simon/TEACH/28000/DavisUniversal.pdf was not found on this server. Lecture Notes in Computer Science, 3988 pp. 125–132
- Hagar, A. and Korolev, A., Quantum Hypercomputation—Hype or Computation? （页面存档备份，存于互联网档案馆）, (2007)
- Müller, Vincent C. On the possibilities of hypercomputing supertasks. Minds and Machines. 2011, 21 (1): 83–96 [2017-12-20]. doi:10.1007/s11023-011-9222-6. （原始内容存档于2017-12-22）.
- Ord, Toby. Hypercomputation: Computing more than the Turing machine can compute （页面存档备份，存于互联网档案馆）: A survey article on various forms of hypercomputation.
- Piccinini, Gualtiero: Computation in Physical Systems （页面存档备份，存于互联网档案馆）
- Putz, Volkmar and Karl Svozil, Can a computer be "pushed" to perform faster-than-light? （页面存档备份，存于互联网档案馆）, (2010)
- Rogers, H. (1987) Theory of Recursive Functions and Effective Computability, MIT Press, Cambridge Massachusetts
- Mike Stannett, Mike. X-machines and the halting problem: Building a super-Turing machine. Formal Aspects of Computing. 1990, 2 (1): 331–341. doi:10.1007/BF01888233.
- Mike Stannett, The case for hypercomputation, Applied Mathematics and Computation, Volume 178, Issue 1, 1 July 2006, Pages 8–24, Special Issue on Hypercomputation
- Syropoulos, Apostolos (2008), Hypercomputation: Computing Beyond the Church–Turing Barrier (preview （页面存档备份，存于互联网档案馆）), Springer. ISBN 978-0-387-30886-9
- Turing, Alan. Systems of logic based on ordinals. Proceedings of the London Mathematical Society. 1939, 45: 161–228. doi:10.1112/plms/s2-45.1.161.