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Turing’s Ideas and Models of Computation

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Alan Turing: Life and Legacy of a Great Thinker

Summary

The theory of computation that we have inherited from the 1960s focuses on algorithmic computation as embodied in the Turing Machine to the exclusion of other types of computation that Turing had considered. In this chapter we present new models of computation, inspired by Turing’s ideas, that are more appropriate for today’s interactive, networked, and embedded computing systems. These models represent super-Turing computation, going beyond Turing Machines and algorithms. We identify three principles underlying super-Turing computation (interaction with the world, infinity of resources, and evolution of systems) and apply these principles in our discussion of the implications of super-Turing computation for the future of computer science.

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References

  1. Back T., Fogel D. B., Michalewicz Z. (eds.), Handbook of Evolutionary Computation, Oxford University Press, 1997.

    Google Scholar 

  2. “Algorithm.” Encyclopedia Britannica 2003 Encyclopedia Britannica Premium Service, http://www.britannica.com/eb/article?eu=5785.

  3. Brooks R. A., Elephants Don’t Play Chess, in P. Maes (ed.), Designing Autonomous Agents: Theory and Practice from Biology to Engineering and Back, The MIT Press, 1994, pp. 3–15.

    Google Scholar 

  4. Burks A., Essays on Cellular Automata, Univ. of Illinois Press, 1970.

    MATH  Google Scholar 

  5. Church A., An Unsolvable Problem of Elementary Number Theory, American Journal of Mathematics, 58:345–363, 1936.

    Article  MathSciNet  Google Scholar 

  6. Church A., Rosser J. B., Some properties of conversion, Transactions of the AMS, 39:472–482, 1936.

    Article  MathSciNet  Google Scholar 

  7. Copeland B. J., Super-Turing Machines, Complexity, 4(l):30–32, 1998.

    Article  MathSciNet  Google Scholar 

  8. Davis M., Why Gödel Didn’t Have Church’s Thesis, Information & Control, .54:3–24, 1982.

    Article  MATH  Google Scholar 

  9. Eberbach E., Brooks R., Phoha S., Flexible Optimization and Evolution of Underwater Autonomous Agents, LNAI 1711, Springer-Verlag, Berlin Heidelberg New York, 1999, pp. 519–527.

    Google Scholar 

  10. Eberbach E., $-Calculus Bounded Rationality = Process Algebra + Anytime Algorithms, in: (ed. J. C. Misra) Applicable Mathematics: Its Perspectives and Challenges, Narosa Publishing House, New Delhi, Mumbai, Calcutta, 2001, pp. 213–220.

    Google Scholar 

  11. Eberbach E., Is Entscheidungsproblem Solvable? Beyond Undecidability of Turing Machines and Its Consequence for Computer Science and Mathematics, in: (ed. J. C. Misra) Computational Mathematics, Modelling and Algorithms, Narosa Publishing House, New Delhi, Chap. 1, 2003, pp. 1–32.

    Google Scholar 

  12. Eberbach E., On Expressiveness of Evolutionary Computation: Is EC Algorithmic?, Proc. 2002 World Congress on Computational Intelligence (WCCI), Honolulu, HI, 2002, pp. 564–569.

    Google Scholar 

  13. Farley B. G., Clark W. A., Simulation of self-organizing systems by digital computer, IRE Transactions on Information Theory, 4:76–84, 1954.

    MathSciNet  Google Scholar 

  14. Fogel D. B. (ed.), Evolutionary Computation: The Fossil Record, IEEE Press, NY, 1998.

    MATH  Google Scholar 

  15. Garzón M., Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks, An EATCS series, Springer-Ver lag, Berlin Heidelberg New York, 1995.

    Book  MATH  Google Scholar 

  16. Gasarch W., Guest Column: The P=?NP Poll, SIGACT News, 33(2):34–47, June 2002.

    Article  Google Scholar 

  17. Gödel K., Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, Monatsheñe für Mathematik und Physik, 38:173–198, 1931.

    Article  Google Scholar 

  18. Goldin D., Persistent Turing Machines as a Model of Interactive Computation, FoIKS’OO, Cottbus, Germany, 2000.

    Google Scholar 

  19. Goldin D., Smolka S., Wegner P., Turing Machines, Transition Systems, and Interaction, proc. 8 th Intl Workshop on Expressiveness in Concurrency, Aalborg, Denmark, August 2001

    Google Scholar 

  20. Hoare C. A. R., Communicating Sequential Processes, Prentice-Hall, 1985.

    MATH  Google Scholar 

  21. Horvitz E., Zilberstein S. (eds.), Computational Tradeoffs under Bounded Resources, Artificial Intelligence, 126:1–196, 2001.

    Google Scholar 

  22. McCulloch W., Pitts W, A Logical Calculus of the Ideas Immanent in Nervous Activity, Bulletin of Mathematical Biophysics, 5:115–133, 1943.

    Article  MathSciNet  MATH  Google Scholar 

  23. Milner R., A Calculus of Communicating Systems, Lecture Notes in Computer Science, 94, Springer-Verlag, Berlin Heidelberg New York, 1980.

    Book  MATH  Google Scholar 

  24. Milner R., Parrow J., Walker D., A Calculus of Mobile Processes, I & II, Information and Computation, 100:1–77, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  25. Milner R., Elements of Interaction, Communications of the ACM, 36(l):78–89, January 1993.

    Article  Google Scholar 

  26. Milner R., Turing, Computing and Communication, a lecture for the 60th anniversary of Turing’s “Entscheidungsproblem” paper, King’s College, Cambridge England, 1997.

    Google Scholar 

  27. Minsky M. L., Theory of Neural-Analog Reinforcement Systems and Its Applications to the Brain-Model Problem, Ph.D. Thesis, Princeton University, 1954.

    Google Scholar 

  28. Penrose R., The Emperor’s New Mind, Oxford, 1989.

    Google Scholar 

  29. Pierce B., Turner D., Piet: A Programming Language Based on the Pi-Calculus, in: Plot kin G. et al (eds.), Proof, Language, and Interaction: Essays in Honour of Robin Milner, The MIT Press, 2000, pp. 455–494.

    Google Scholar 

  30. Plotkin G., Stirling C, Tofte M. (eds.), Proof, Language, and Interaction: Essays in Honour of Robin Milner, The MIT Press, 2000.

    Google Scholar 

  31. Rosenblatt F., The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain, Psychological Review, 65:386–408, 1958.

    Article  MathSciNet  Google Scholar 

  32. Russell S., Norvig P., Artificial Intelligence: A Modern Approach, 2nd edition, Prentice-Hall, 2003.

    Google Scholar 

  33. Samuel A. L., Some studies in machine learning using the game of checkers, IBM Journal of Research and Development, 3:211–229, 1959.

    Article  MathSciNet  Google Scholar 

  34. Siegelmann H., Neural Networks and Analog Computation: Beyond the Turing Limit, Birkhauser, 1999.

    Book  MATH  Google Scholar 

  35. Simon, H. A. The Sciences of the Artificial. MIT Press, 1969.

    Google Scholar 

  36. Sipser, M. Introduction to the Theory of Computation, PWS Publishing Company, 1997.

    MATH  Google Scholar 

  37. Teuscher C, Turing’s Connectionism: An Investigation of Neural Network Architectures, Springer-Ver lag, London, 2002.

    Google Scholar 

  38. Turing A., On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, series 2, 42:230–265, 1936–37.

    Google Scholar 

  39. Turing A., Systems of Logic based on Ordinals, Proceedings of the London Mathematical Society, series 2, 45:161–228, 1939.

    Google Scholar 

  40. Turing A., The ACE Report, in A. M. Turing’s Ace Report of 1946 and Other Papers, eds. B. E. Carpenter and R. W. Doran, MIT Press, 1986.

    Google Scholar 

  41. Turing A., Lecture to the London Math. Society on 20’th February 1947, in A. M. Turing’s Ace Report of 1946 and Other Papers, eds. B. E. Carpenter and R. W. Doran, MIT Press, 1986.

    Google Scholar 

  42. Turing A., Intelligent Machinery, 1948; in Collected Works of A. M. Turing: Mechanical Intelligence, ed. D. C. Ince, Elsevier Science, 1992.

    Google Scholar 

  43. Turing A., Computing Machinery and Intelligence, Mind, 59(236):433–460, 1950.

    Article  MathSciNet  Google Scholar 

  44. Turing A., The Chemical Basis of Morphogenesis, Philosophical Transactions of the Royal Society of London, B 237:37–72, 1952.

    Article  Google Scholar 

  45. Van Leeuwen J., Wiedermann J., The Turing Machine Paradigm in Contemporary Computing, in. B. Enquist and W. Schmidt (eds.) Mathematics Unlimited — 2001 and Beyond, LNCS, Springer-Verlag, Berlin Heidelberg New York, 2000.

    Google Scholar 

  46. Von Neumann J., Theory of Self-Reproducing Automata, (edited and completed by Burks A. W.), Univ. of Illinois Press, 1966.

    Google Scholar 

  47. Wegner P., Why Interaction is More Powerful Than Algorithms, Communications of the ACM, 40(5):81–91, 1997.

    Article  Google Scholar 

  48. Wegner P., Interactive Foundations of Computing, Theoretical Computer Science, 192:315–351, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  49. Wegner P., Goldin D., Coinductive Models of Finite Computing Agents, Workshop on Coinductive Methods in Computer Science, Electronic Notes in Theoretical Computer Science, Amsterdam, March 1999.

    Google Scholar 

  50. Wegner P., Goldin D., Interaction as a Framework for Modeling, LNCS 1565, April 1999.

    Google Scholar 

  51. Wegner P., Goldin D., Computation Beyond Turing Machines, Communications of the ACM, April 2003.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer and Information Science Department, University of Massachusetts, USA

    Eugene Eberbach

  2. Computer Science &; Engineering Department, University of Connecticut, USA

    Dina Goldin

  3. Department of Computer Science, Brown University, USA

    Peter Wegner

Authors
  1. Eugene Eberbach
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  2. Dina Goldin
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  3. Peter Wegner
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Editor information

Editors and Affiliations

  1. Logic Systems Laboratory, EPFL-IC-LSL, Swiss Federal Institute of Technology Lausanne (EPFL), 1015, Lausanne, Switzerland

    Christof Teuscher

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Eberbach, E., Goldin, D., Wegner, P. (2004). Turing’s Ideas and Models of Computation. In: Teuscher, C. (eds) Alan Turing: Life and Legacy of a Great Thinker. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05642-4_7

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  • DOI: https://doi.org/10.1007/978-3-662-05642-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05744-1

  • Online ISBN: 978-3-662-05642-4

  • eBook Packages: Springer Book Archive

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