Minds and Machines

, Volume 18, Issue 1, pp 17–38

The Interactive Nature of Computing: Refuting the Strong Church–Turing Thesis

Article

Abstract

The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a new paradigm is hindered by the Strong Church–Turing Thesis (SCT), the widespread belief that Turing Machines (TMs) capture all computation, so models of computation more expressive than TMs are impossible. In this paper, we show that SCT reinterprets the original Church–Turing Thesis (CTT) in a way that Turing never intended; its commonly assumed equivalence to the original is a myth. We identify and analyze the historical reasons for the widespread belief in SCT. Only by accepting that it is false can we begin to adopt interaction as an alternative paradigm of computation. We present Persistent Turing Machines (PTMs), that extend TMs to capture sequential interaction. PTMs allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of TMs and of the CTT. The paradigm shift to interaction provides an alternative understanding of the nature of computing that better reflects the services provided by today’s computing technology.

Keywords

Interactive computation Church–Turing Thesis Turing Machines Strong Church–Turing Thesis Persistent Turing Machines Sequential Interaction Thesis Computation expressiveness Paradigm shift 

References

  1. ACM Curriculum Committee on Computer Science. (1965). An undergraduate program in computer science—preliminary recommendations. Communications of the ACM, 8(9), 543–552.Google Scholar
  2. ACM Curriculum Committee on Computer Science. (1969). Curriculum 68: Recommendations for academic programs in computer science. Communications of the ACM, 11(3), 151–197.Google Scholar
  3. Brooks, R. (1991). Intelligence without reason. Technical Report 1293. MIT Artificial Intelligence Lab. Cambridge, MA.Google Scholar
  4. Cleland, E. C. (2004). The concept of computability. Theoretical Computer Science, 317(1–3), 209–225.Google Scholar
  5. Cleland, E. C. (2007). In A. Olszewski (Eds.), The Church–Turing Thesis: A last vestige of a failed mathematical program (pp. 119–149).Google Scholar
  6. Copeland, B. J. (1997). The Church–Turing Thesis. Stanford Encyclopedia of Philosophy (substantially revised in 2005).Google Scholar
  7. Copeland, B. J. (2002). Hypercomputation. Minds and Machines, 12(4), 461–502.MATHCrossRefGoogle Scholar
  8. Davis, M. (1958). Computability & unsolvability. McGraw-Hill.Google Scholar
  9. Denning, P. (2004). The field of programmers myth. Communications of the ACM, 47(7).Google Scholar
  10. Dijkstra, E. W. (1968). Go to statement considered harmful. Communications of the ACM, 11(3), 147–148.CrossRefMathSciNetGoogle Scholar
  11. Eberbach, E., Goldin, D., & Wegner, P. (2004). Turing’s ideas and models of computation. In C. Teuscher (Ed.), Alan turing: Life and legacy of a great thinker. Springer.Google Scholar
  12. Fischer, M. J., & Stockmeyer, L. J. (1974). Fast on-line integer multiplication. Journal of Computer and System Sciences, 9(3), 317–331.MATHMathSciNetGoogle Scholar
  13. Fitz, H. (2007). In A. Olszewski, et al. (Eds.), Church’s thesis and physical computation (pp. 175–219).Google Scholar
  14. Goldin, D., Smolka, S., Attie, P., & Sonderegger, E. (2004). Turing Machines, transition systems, and interaction. Information & Computation Journal, 194(2), 101–128.MATHCrossRefMathSciNetGoogle Scholar
  15. Goldin, D., & Wegner, P. (2005). The Church–Turing Thesis: Breaking the myth. LNCS 3526 (pp. 152–168). Springer.Google Scholar
  16. Goldwasser, S., Micali, S., & Rackoff, C. (1989). The knowledge complexity of interactive proof systems. SIAM Journal of Computing, 18(1), 186–208.MATHCrossRefMathSciNetGoogle Scholar
  17. Hopcroft, J. E., & Ullman, J. D. (1969). Formal languages and their relation to automata. Addison-Wesley.Google Scholar
  18. Knuth, D. (1968). The art of computer programming, Vol. 1: Fundamental algorithms. Addison-Wesley.Google Scholar
  19. Kugel, P. (2002). Computing machines can’t be intelligent (...and Turing said so). Minds and Machines, 12(4), 563–579.MATHCrossRefGoogle Scholar
  20. Lynch, N. A., & Tuttle M. R. (1989). An introduction to input/output automata. CWI Quarterly, 2(3), 219–246. Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands.Google Scholar
  21. Olszewski, A., & Wolenski, J., et. al. (Eds.) (2006). Church’s thesis after 70 years. Ontos-Verlag.Google Scholar
  22. Papadimitriou, C. H. (1995). Database metatheory: Asking the big queries. In Proceedings of the 14th ACM Symposium on Principles of Database Systems, San Jose, CA.Google Scholar
  23. Rice, J. K., & Rice J. R. (1969). Introduction to computer science: Problems, algorithms, languages, information and computers. USA: Holt, Rinehart and Winston.Google Scholar
  24. Russell, S., & Norveig, P. (1994). Artificial intelligence: A modern approach. Addison-Wesley.Google Scholar
  25. SIGACT News. (2004). ACM Press, p. 49.Google Scholar
  26. Sieg, W. (2005). Computability and discrete dynamical systems. LNCS 3526 (pp. 440–440). Springer.Google Scholar
  27. Sipser, M. (2005). Introduction to the theory of computation (2nd ed.). PWS Publishing Company.Google Scholar
  28. Turing, A. (1936). On computable numbers, with an application to the Entscheidungs problem. Proceedings of the London Mathematical Society, 42(2), 230–265; A correction, ibid, 43, 544–546.Google Scholar
  29. van Leeuwen, J., & Wiedermann, J. (2000). The turing machine paradigm in contemporary computing. In B. Enquist & W. Schmidt (Eds.), Mathematics unlimited—2001 and beyond. LNCS. Springer-Verlag.Google Scholar
  30. Weger, P. (1968). Programming languages, information structures and machine organization. McGraw-Hill.Google Scholar
  31. Wegner, P. (1997). Why interaction is more powerful than algorithms. Communications of the ACM, 40, 80–91.CrossRefGoogle Scholar
  32. Wegner, P. (1998). Interactive foundations of computing. Theoretical Computer Science, 19(2), 315–351.CrossRefMathSciNetGoogle Scholar
  33. Wegner, P. (1999). Towards empirical computer science. The Monist, 82(1), 58–108.MathSciNetGoogle Scholar
  34. Wegner, P., & Goldin, D. (2003). Computation beyond Turing Machines. Communications of the ACM, 46, 100–102.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Computer Science DepartmentBrown UniversityProvidenceUSA

Personalised recommendations