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Complexity of Evolving Interactive Systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3113))

Abstract

We study a versatile model of evolving interactive computing: lineages of automata. A lineage consists of a sequence of interactive finite automata, with a mechanism of passing information from each automaton to its immediate successor. Lineages enable a definition of a suitable complexity measure for evolving systems. We show several complexity results, including a hierarchy result.

The research of the third author was partially supported by GA ČR grant No. 201/02/1456.

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References

  1. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural Complexity I, 2nd edn. Springer, Berlin (1995)

    Google Scholar 

  2. Landweber, L.H.: Decision Problems for ω-Automata. Math. Syst. Theory 3(4), 376–384 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  3. 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 

  4. van Leeuwen, J., Wiedermann, J.: The Turing Machine Paradigm in Contemporary Computing. In: Enquist, B., Schmidt, W. (eds.) Mathematics Unlimited - 2001 and Beyond, pp. 1139–1156. Springer, Heidelberg (2001)

    Google Scholar 

  5. van Leeuwen, J., Wiedermann, J.: A Computational Model of Interaction in Embedded Systems. in: Technical Report UU-CS-2001-02, Institute of Information and Computing Sciences, Utrecht University (2001)

    Google Scholar 

  6. 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 

  7. Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications, 2nd edn. Springer, New York (1997)

    MATH  Google Scholar 

  8. Staiger, L.: ω-Languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages. Beyond Words, vol. 3, pp. 339–387. Springer, Berlin (1997)

    Google Scholar 

  9. Thomas, W.: Automata on Infinite Objects. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 134–191. Elsevier Science, Amsterdam (1990)

    Google Scholar 

  10. Verbaan, P., van Leeuwen, J., Wiedermann, J.: Lineages of Automata, Technical Report UU-CS-2004-018, Institute of Information and Computing Sciences, Utrecht University (2004)

    Google Scholar 

  11. Wegner, P.: Why Interaction is more Powerful than Algorithms. Comm. of the ACM 40(5), 81–91 (1997)

    Article  Google Scholar 

  12. Wegner, P., Eberbach, E.: New Models of Computation. The Computer Journal 47(1), 4–9 (2004)

    Article  MATH  Google Scholar 

  13. Wegner, P., Goldin, D.: Computations beyond TuringMachines. Comm. of the ACM 46, 100–102 (2003)

    Article  Google Scholar 

  14. Wiedermann, J., van Leeuwen, J.: Emergence of a Super-Turing Computational Potential in Artificial Living Systems. In: Kelemen, J., Sosík, P. (eds.) ECAL 2001. LNCS (LNAI), vol. 2159, pp. 55–65. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Wiedermann, J., van Leeuwen, J.: The Emergent Computational Potential of Evolving Artificial Living Systems. AI Communications 15(4), 205–215 (2002)

    MathSciNet  Google Scholar 

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Verbaan, P., van Leeuwen, J., Wiedermann, J. (2004). Complexity of Evolving Interactive Systems. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Theory Is Forever. Lecture Notes in Computer Science, vol 3113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27812-2_24

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  • DOI: https://doi.org/10.1007/978-3-540-27812-2_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22393-1

  • Online ISBN: 978-3-540-27812-2

  • eBook Packages: Springer Book Archive

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