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On the Executability of Interactive Computation

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Pursuit of the Universal (CiE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9709))

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Abstract

The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are reactively executable. In this article we provide a comparison of the two models. We show, on the one hand, that the behaviour exhibited by ITMs is reactively executable, and, on the other hand, that the stream translations naturally associated with RTMs are interactively computable. We conclude from these results that the theory of reactive executability subsumes the theory of interactive computability. Inspired by the existing model of ITMs with advice, which provides a model of evolving computation, we also consider RTMs with advice and we establish that a facility of advice considerably upgrades the behavioural expressiveness of RTMs: every countable transition system can be simulated by some RTM with advice up to a fine notion of behavioural equivalence.

F. Yang—This author is sponsored by the China Scholarship Council (CSC).

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References

  1. Aceto, L., Ingólfsdóttir, A., Larsen, K.G., Srba, J.: Reactive Systems-Modelling, Specification and Verification. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  2. Baeten, J.C.M., Cuijpers, P.J.L., Luttik, B., van Tilburg, P.J.A.: A process-theoretic look at automata. In: Arbab, F., Sirjani, M. (eds.) FSEN 2009. LNCS, vol. 5961, pp. 1–33. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Baeten, J.C.M., Luttik, B., van Tilburg, P.: Reactive Turing machines. Inf. Comput. 231, 143–166 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cabessa, J., Villa, A.E.P.: The super-Turing computational power of interactive evolving recurrent neural networks. In: Mladenov, V., Koprinkova-Hristova, P., Palm, G., Villa, A.E.P., Appollini, B., Kasabov, N. (eds.) ICANN 2013. LNCS, vol. 8131, pp. 58–65. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. J. ACM (JACM) 43(3), 555–600 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. van Glabbeek, R., Luttik, B., Trčka, N.: Branching bisimilarity with explicit divergence. Fundam. Informaticae 93(4), 371–392 (2009)

    MathSciNet  MATH  Google Scholar 

  7. van Glabbeek, R.J.: The linear time — branching time spectrum II. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)

    Google Scholar 

  8. Goldin, D., Smolka, S.A., Wegner, P.: Interactive Computation: The New Paradigm. Springer, Heidelberg (2006)

    Book  MATH  Google Scholar 

  9. van Leeuwen, J., Wiedermann, J.: On algorithms and interaction. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 99–113. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. van Leeuwen, J., Wiedermann, J.: Beyond the Turing limit: evolving interactive systems. In: Pacholski, L., Ružička, P. (eds.) SOFSEM 2001. LNCS, vol. 2234, pp. 90–109. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. van Leeuwen, J., Wiedermann, J.: The Turing machine paradigm in contemporary computing. In: Enquist, B., Schmidt, W. (eds.) Mathematics Unlimited-2001 and Beyond. LNCS, vol. 2001, pp. 1139–1155. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. van Leeuwen, J., Wiedermann, J.: A theory of interactive computation. In: Goldin, D., Smolka, S.A., Wegner, P. (eds.) Interactive Computation, pp. 119–142. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Luttik, B., Yang, F.: Executability and the \(\pi \)-calculus (extended abstract). In: Proceedings of ICE 2015, pp. 37–52 (2015)

    Google Scholar 

  14. Luttik, B., Yang, F.: On the Executability of Interactive Computation. CoRR abs/1601.01546 (2016). http://arxiv.org/abs/1601.01546

  15. Turing, A.M.: On computable numbers, with an application to the Entscheidungs-problem. J. Math. 58, 345–363 (1936)

    Article  Google Scholar 

  16. Verbaan, P.R.A.: The computational complexity of evolving systems. Ph.D. thesis, Utrecht University (2006)

    Google Scholar 

  17. Wiedermann, J., van Leeuwen, J.: How we think of computing today. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds.) CiE 2008. LNCS, vol. 5028, pp. 579–593. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Bas Luttik & Fei Yang

Authors
  1. Bas Luttik
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  2. Fei Yang
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Correspondence to Fei Yang .

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Editors and Affiliations

  1. Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. Université Paris-Diderot - Paris 7, Paris, France

    Laurent Bienvenu

  3. University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

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Luttik, B., Yang, F. (2016). On the Executability of Interactive Computation. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_32

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  • DOI: https://doi.org/10.1007/978-3-319-40189-8_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40188-1

  • Online ISBN: 978-3-319-40189-8

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