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On Algorithms and Interaction

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Book cover Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

Abstract

Many IT-systems behave very differently from classical machine models: they interact with an unpredictable environment, they never terminate, and their behavior changes over time. Wegner [25, 26] (see also [28]) recently argued that the power of interaction goes beyond the Church-Turing thesis. To explore interaction from a computational viewpoint, we describe a generic model of an ‘interactive machine’ which interacts with the environment using single streams of input and output signals over a simple alphabet. The model uses ingredients from the theory of ω-automata. Viewing the interactive machines as transducers of infinite streams of signals, we show that their interactive recognition and generation capabilities are identical. It is also shown that, in the given model, all interactively computable functions are limit-continuous.

This research was partially supported by GA ČR grant No. 201/98/0717 and by EC Contract IST-1999-14186 (Project ALCOM-FT).

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References

  1. M. Broy. A logical basis for modular software and systems engineering, in: B. Rovan (Ed.), SOFSEM’98: Theory and Practice of Informatics, Proc. 25th Conference on Current Trends, Lecture Notes in Computer Science, Vol. 1521, Springer-Verlag, Berlin, 1998, pp. 19–35.

    Google Scholar 

  2. R.S. Cohen, A.Y. Gold. ω-Computations on Turing machines, Theor. Comput. Sci. 6 1978 1–23.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Engelfriet, H.J. Hoogeboom. X-automata on ω-words, Theor. Comput. Sci. 110 1993 1–51.

    Article  MATH  MathSciNet  Google Scholar 

  4. D.Q. Goldin. Persistent Turing machines as a model of interactive computation, in: K-D. Schewe and B. Thalheim (Eds.), Foundations of Information and Knowledge Systems, Proc. First Int. Symposium (FoIKS 2000), Lecture Notes in Computer Science, vol. 1762, Springer-Verlag, Berlin, 2000, pp. 116–135.

    Chapter  Google Scholar 

  5. D. Goldin, P. Wegner. Persistence as a form of interaction, Techn. Rep. CS-98-07, Dept. of Computer Science, Brown University, Providence, RI, 1998.

    Google Scholar 

  6. D. König. Sur les correspondances multivoques des ensembles, Fundam. Math. 8 1926 114–134.

    MATH  Google Scholar 

  7. D. König. Über eine Schlussweise aus dem Endlichen ins Unendliche (Punktmengen.-Kartenfärben.-Verwantschaftsbeziehungen.-Schachspiel), Acta Litt. Sci. (Sectio Sci. Math.) 3 1927 121–130.

    Google Scholar 

  8. S. Kosub. Persistent computations, Technical Report No. 217, Institut für Informatik, Julius-Maximilians-Universität Würzburg, 1998.

    Google Scholar 

  9. Z. Manna, A. Pnueli. Models for reactivity, Acta Informatica 30 1993 609–678.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Milner. A calculus of communicating systems, Lecture Notes in Computer Science, Vol. 92, Springer-Verlag, Berlin, 1980.

    MATH  Google Scholar 

  11. R. Milner. Elements of interaction, C.ACM 36:1 1993 78–89.

    Google Scholar 

  12. A. Pnueli. Applications of temporal logic to the specification and verification of reactive systems: a survey of current trends, in: J.W. de Bakker, W.-P. de Roever and G. Rozenberg, Current Trends in Concurrency, Lecture Notes in Computer Science, Vol. 224, Springer-Verlag, Berlin, 1986, pp. 510–585.

    Chapter  Google Scholar 

  13. A. Pnueli. Specification and development of reactive systems, in: H.-J. Kugler (Ed.), Information Processing 86, Proceedings IFIP 10th World Computer Congress, Elsevier Science Publishers (North-Holland), Amsterdam, 1986, pp. 845–858.

    Google Scholar 

  14. M. Prasse, P. Rittgen. Why Church’s Thesis still holds. Some notes on Peter Wegner’s tracts on interaction and computability, The Computer Journal 41 1998 357–362.

    Article  MATH  Google Scholar 

  15. L. Staiger. ω-Languages, in: G. Rozenberg and A. Salomaa (Eds.), Handbook of Formal Languages, Vol. 3: Beyond Words, Chapter 6, Springer-Verlag, Berlin, 1997, pp. 339–387.

    Google Scholar 

  16. W. Thomas. Automata on infinite objects, in: J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, Vol. B: Models and Semantics, Elsevier Science Publishers, Amsterdam, 1990, pp. 135–191.

    Google Scholar 

  17. W. Thomas. Languages, automata, and logic, in: G. Rozenberg and A. Salomaa (Eds.), Handbook of Formal Languages, Vol. 3: Beyond Words, Chapter, Springer-Verlag, Berlin, 1997, pp. 389–455.

    Google Scholar 

  18. B.A. Trakhtenbrot. Automata and their interaction: definitional suggestions, in: G. Ciobanu and G. Păun (Eds.), Fundamentals of Computation Theory, Proc. 12th International Symposium (FCT’99), Lecture Notes in Computer Science, Vol. 1684, Springer-Verlag, Berlin, 1999, pp. 54–89.

    Chapter  Google Scholar 

  19. J. van Leeuwen, J. Wiedermann. A computational model of interaction, Technical Report, Dept of Computer Science, Utrecht University, Utrecht, 2000.

    Google Scholar 

  20. J. van Leeuwen, J. Wiedermann. Breaking the Turing barrier: the case of the Internet, Technical Report, Inst. of Computer Science, Academy of Sciences, Prague, 2000.

    Google Scholar 

  21. J. van Leeuwen, J. Wiedermann. Extending the Turing Machine Paradigm, in: B. Engquist and W. Schmidt (Eds.), Mathematics Unlimited-2001 and Beyond, Springer-Verlag, Berlin, 2000 (to appear).

    Google Scholar 

  22. K. Wagner, L. Staiger. Recursive ω-languages, in: M. Karpinsky (Ed.), Fundamentals of Computation Theory, Proc. 1977 Int. FCT-Conference, Lecture Notes in Computer Science, Vol. 56, Springer-Verlag, Berlin, 1977, pp. 532–537.

    Google Scholar 

  23. P. Wegner. Interactive foundations of object-based programming, IEEE Computer 28:10 1995 70–72.

    Google Scholar 

  24. P. Wegner. Interaction as a basis for empirical computer science, Comput. Surv. 27 1995 45–48.

    Article  Google Scholar 

  25. P. Wegner. Why interaction is more powerful than algorithms, C.ACM 40 1997 80–91.

    Article  Google Scholar 

  26. P. Wegner. Interactive foundations of computing, Theor. Comp. Sci. 192 1998 315–351.

    Article  MATH  MathSciNet  Google Scholar 

  27. P. Wegner, D. Goldin. Co-inductive models of finite computing agents, in: B. Jacobs and J. Rutten (Eds.), CMCS’99-Coalgebraic Methods in Computer Science, TCS: Electronic Notes in Theoretical Computer Science, Vol. 19, Elsevier, 1999.

    Google Scholar 

  28. P. Wegner, D. Goldin. Interaction as a framework for modeling, in: P. Chen et al. (Eds.), Conceptual Modeling-Current Issues and Future Directions, Lecture Notes in Computer Science, Vol. 1565, Springer-Verlag, Berlin, 1999, pp 243–257.

    Google Scholar 

  29. P. Wegner, D.Q. Goldin. Interaction, comput ability, and Church’s thesis, The Computer Journal 1999 (to appear).

    Google Scholar 

  30. G. Winskel. The formal semantics of programming languages: an introduction, The MIT Press, Cambridge (Mass.), 1993.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Utrecht University, Padualaan 14, 3584, CH Utrecht, the Netherlands

    Jan van Leeuwen

  2. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jiří Wiedermann

Authors
  1. Jan van Leeuwen
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  2. Jiří Wiedermann
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

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© 2000 Springer-Verlag Berlin Heidelberg

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van Leeuwen, J., Wiedermann, J. (2000). On Algorithms and Interaction. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_7

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  • DOI: https://doi.org/10.1007/3-540-44612-5_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

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