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超计算

2018-08-30 10:00:05     所属分类:计算理论

超计算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", (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 (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. doi:10.1016/j.amc.2005.09.072. 
  • Cooper, S. B.; Odifreddi, P. Incomputability in Nature. (编) S. B. Cooper and S. S. Goncharov. Computability and Models: Perspectives East and West (PDF). Plenum Publishers, New York, Boston, Dordrecht, London, Moscow. 2003: 137–160. 
  • 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?, (2007)
  • Müller, Vincent C. On the possibilities of hypercomputing supertasks. Minds and Machines. 2011, 21 (1): 83–96. doi:10.1007/s11023-011-9222-6. 
  • Ord, Toby. Hypercomputation: Computing more than the Turing machine can compute: A survey article on various forms of hypercomputation.
  • Piccinini, Gualtiero: Computation in Physical Systems
  • Putz, Volkmar and Karl Svozil, Can a computer be "pushed" to perform faster-than-light?, (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), 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. 

外部链接

  • Hypercomputation Research Network

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