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The Church-Turing Thesis: Breaking the Myth

  • Dina Goldin
  • Peter Wegner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

According to the interactive view of computation, communication happens during the computation, not before or after it. This approach, distinct from concurrency theory and the theory of computation, represents a paradigm shift that changes our understanding of what is computation and how it is modeled. Interaction machines extend Turing machines with interaction to capture the behavior of concurrent systems, promising to bridge these two fields. This promise is hindered by the widespread belief, incorrectly known as the Church-Turing thesis, that no model of computation more expressive than Turing machines can exist. Yet Turing’s original thesis only refers to the computation of functions and explicitly excludes other computational paradigms such as interaction. In this paper, we identify and analyze the historical reasons for this widespread belief. Only by accepting that it is false can we begin to properly investigate formal models of interaction machines. We conclude the paper by presenting one such model, Persistent Turing Machines (PTMs). PTMs capture sequential interaction, which is a limited form of concurrency; they allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of Turing machines and of the Church-Turing thesis.

Keywords

Turing Machine Input String Theoretical Computer Science Interaction Machine Interactive Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    An Undergraduate Program in Computer Science-Preliminary Recommendations, A Report from the ACM Curriculum Committee on Computer Science. Comm. ACM 8(9), 543–552 (1965)Google Scholar
  2. 2.
    Curriculum 68: Recommendations for Academic Programs in Computer Science, A Report of the ACM Curriculum Committee on Computer Science. Comm. ACM 11(3), 151–197 (1968)Google Scholar
  3. 3.
    Brooks, R.: Intelligence Without Reason. MIT AI Lab Technical Report 1293Google Scholar
  4. 4.
    Davis, M.: Computability & Unsolvability. McGraw-Hill, New York (1958)zbMATHGoogle Scholar
  5. 5.
    Denning, P.: The Field of Programmers Myth. Comm. ACM (July 2004)Google Scholar
  6. 6.
    Eberbach, E., Goldin, D., Wegner, P.: Turing’s Ideas and Models of Computation. In: Teuscher, C. (ed.) Alan Turing: Life and Legacy of a Great Thinker. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comp. 18(1), 186–208 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Goldin, D., Smolka, S., Attie, P., Sonderegger, E.: Turing Machines, Transition Systems, and Interaction. Information & Computation J. (November 2004)Google Scholar
  9. 9.
    Hopcroft, J.E., Ullman, J.D.: Formal languages and their relation to automata. Addison-Wesley, Reading (1969)zbMATHGoogle Scholar
  10. 10.
    Knuth, D.: The Art of Computer Programming. Fundamental Algorithms, vol. 1. Addison-Wesley, Reading (1968)zbMATHGoogle Scholar
  11. 11.
    Lynch, N., Tuttle, M.: An Introduction to Input/Output automata. CWI Quarterly 2(3), 219–246 (1989); Centrum voor Wiskunde en Informatica, Amsterdam, The NetherlandsGoogle Scholar
  12. 12.
    Rice, J.K., Rice, J.N.: Computer Science: Problems, Algorithms, Languages, Information and Computers. Holt, Rinehart and Winston (1969)Google Scholar
  13. 13.
    Russell, S., Norveig, P.: Artificial Intelligence: A Modern Approach. Addison-Wesley, Reading (1994)Google Scholar
  14. 14.
    Rogers Jr., H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)zbMATHGoogle Scholar
  15. 15.
    Sanchis, L.: Recursive Functionals. North-Holland, Amsterdam (1992)zbMATHGoogle Scholar
  16. 16.
    SIGACT News, p. 49. ACM Press, New York (March 2004)Google Scholar
  17. 17.
    Sipser, M.: Introduction to the Theory of Computation. PWS Publishing Company (1997)Google Scholar
  18. 18.
    Turing, A.: On Computable Numbers, with an Application to the Entscheidungsproblem. Proc. London Math. Soc. 42(2), 230–265 (1936); A correction, ibid 43, 544-546 (1937) Google Scholar
  19. 19.
    van Leeuwen, J., Wiedermann, J.: The Turing Machine Paradigm in Contemporary Computing. In: Enquist, B., Schmidt, W. (eds.) Mathematics Unlimited - 2001 and Beyond. Springer, Heidelberg (2000)Google Scholar
  20. 20.
    Wegner, P.: Programming Languages, Information Structures and Machine Organization. McGraw-Hill, New York (1968)Google Scholar
  21. 21.
    Wegner, P.: Why Interaction is More Powerful Than Algorithms. Comm. ACM (May 1997)Google Scholar
  22. 22.
    Wegner, P.: Interactive Foundations of Computing. Theoretical Computer Science 192 (February 1998)Google Scholar
  23. 23.
    Wegner, P., Goldin, D.: Computation Beyond Turing Machines. Comm. ACM (April 2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dina Goldin
    • 1
  • Peter Wegner
    • 2
  1. 1.Computer Science & Engineering DepartmentUniversity of ConnecticutStorrsUSA
  2. 2.Computer Science DepartmentBrown UniversityProvidenceUSA

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