Dina Goldin
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.
- 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
Digital Library
- 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 ScholarDigital Library
- Brooks, R. (1991). Intelligence without reason . Technical Report 1293. MIT Artificial Intelligence Lab. Cambridge, MA. Google ScholarDigital Library
- Cleland, E. C. (2004). The concept of computability. Theoretical Computer Science, 317 (1-3), 209-225. Google ScholarDigital Library
- 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
- Copeland, B. J. (1997). The Church-Turing Thesis. Stanford Encyclopedia of Philosophy (substantially revised in 2005).Google Scholar
- Copeland, B. J. (2002). Hypercomputation. Minds and Machines, 12 (4), 461-502. Google ScholarDigital Library
- Davis, M. (1958). Computability & unsolvability . McGraw-Hill.Google Scholar
- Denning, P. (2004). The field of programmers myth. Communications of the ACM, 47 (7). Google ScholarDigital Library
- Dijkstra, E. W. (1968). Go to statement considered harmful. Communications of the ACM, 11 (3), 147-148. Google ScholarDigital Library
- 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
- Fischer, M. J., & Stockmeyer, L. J. (1974). Fast on-line integer multiplication. Journal of Computer and System Sciences, 9 (3), 317-331.Google ScholarDigital Library
- Fitz, H. (2007). In A. Olszewski, et al. (Eds.), Church's thesis and physical computation (pp. 175-219).Google Scholar
- Goldin, D., Smolka, S., Attie, P., & Sonderegger, E. (2004). Turing Machines, transition systems, and interaction. Information & Computation Journal, 194 (2), 101-128. Google ScholarDigital Library
- Goldin, D., & Wegner, P. (2005). The Church-Turing Thesis: Breaking the myth . LNCS 3526 (pp. 152- 168). Springer. Google ScholarDigital Library
- Goldwasser, S., Micali, S., & Rackoff, C. (1989). The knowledge complexity of interactive proof systems. SIAM Journal of Computing, 18 (1), 186-208. Google ScholarDigital Library
- Hopcroft, J. E., & Ullman, J. D. (1969). Formal languages and their relation to automata . Addison-Wesley. Google ScholarDigital Library
- Knuth, D. (1968). The art of computer programming, Vol. 1: Fundamental algorithms . Addison-Wesley.Google ScholarDigital Library
- Kugel, P. (2002). Computing machines can't be intelligent (..and Turing said so). Minds and Machines, 12 (4), 563-579. Google ScholarDigital Library
- Lynch, N. A., & Turtle 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
- Olszewski, A., & Wolenski, J., et. al. (Eds.) (2006). Church's thesis after 70 years . Ontos-Verlag. Google ScholarDigital Library
- 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 ScholarDigital Library
- Rice, J. K., & Rice J. R. (1969). Introduction to computer science: Problems, algorithms, languages, information and computers . USA: Holt, Rinehart and Winston.Google Scholar
- Russell, S., & Norveig, P. (1994). Artificial intelligence: A modern approach . Addison-Wesley. Google ScholarDigital Library
- SIGACT News . (2004). ACM Press, p. 49.Google Scholar
- Sieg, W. (2005). Computability and discrete dynamical systems . LNCS 3526 (pp. 440-440). Springer. Google ScholarDigital Library
- Sipser, M. (2005). Introduction to the theory of computation (2nd ed.). PWS Publishing Company. Google ScholarDigital Library
- 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
- 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
- Weger, P. (1968). Programming languages, information structures and machine organization . McGraw-Hill. Google ScholarDigital Library
- Wegner, P. (1997). Why interaction is more powerful than algorithms. Communications of the ACM, 40 , 80-91. Google ScholarDigital Library
- Wegner, P. (1998). Interactive foundations of computing. Theoretical Computer Science. 19 (2), 315-351. Google ScholarDigital Library
- Wegner, P. (1999). Towards empirical computer science. The Monist, 82 (1), 58-108.Google ScholarCross Ref
- Wegner, P., & Goldin, D. (2003). Computation beyond Turing Machines. Communications of the ACM, 46 , 100-102. Google ScholarDigital Library
Index Terms
- The Interactive Nature of Computing: Refuting the Strong Church---Turing Thesis
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