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Slightly Beyond Turing’s Computability for Studying Genetic Programming

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Machines, Computations, and Universality (MCU 2007)

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Abstract

Inspired by genetic programming (GP), we study iterative algorithms for non-computable tasks and compare them to naive models. This framework justifies many practical standard tricks from GP and also provides complexity lower-bounds which justify the computational cost of GP thanks to the use of Kolmogorov’s complexity in bounded time.

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References

  1. Banzhaf, W., Langdon, W.B.: Some considerations on the reason for bloat. Genetic Programming and Evolvable Machines 3(1), 81–91 (2002)

    Article  MATH  Google Scholar 

  2. Blickle, T., Thiele, L.: Genetic programming and redundancy. In: Hopf, J. (ed.) Genetic Algorithms Workshop at KI-94. Max-Planck-Institut für Informatik, pp. 33–38 (1994)

    Google Scholar 

  3. Buhrman, H., Fortnow, L., Laplante, S.: Resource-bounded kolmogorov complexity revisited. SIAM Journal on Computing (2001)

    Google Scholar 

  4. Fortnow, L., Kummer, M.: Resource-bounded instance complexity. Theoretical Computer Science A 161, 123–140 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gustafson, S.M., Langdon, W., Koza, J.: Bibliography on genetic programming. In: The Collection of Computer Science Bibliographies (2007)

    Google Scholar 

  6. Hamkins, J.D.: Infinite time turing machines. Minds Mach. 12(4), 521–539 (2002)

    Article  MATH  Google Scholar 

  7. Khintchine, A.Y.: Sur la loi forte des grands nombres. Comptes Rendus de l’Academie des Sciences, 186 (1928)

    Google Scholar 

  8. Kolmogorov, A.N.: Logical basis for information theory and probability theory. IEEE trans. Inform. Theory IT-14, 662–664 (1968)

    Article  MathSciNet  Google Scholar 

  9. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, USA (1992)

    MATH  Google Scholar 

  10. Lugosi, G., Devroye, L., Györfi, L.: A probabilistic theory of pattern recognition. Springer, Heidelberg (1997)

    Google Scholar 

  11. Langdon, W.B.: The evolution of size in variable length representations. In: ICEC 1998, pp. 633–638. IEEE Computer Society Press, Los Alamitos (1998)

    Google Scholar 

  12. Langdon, W.B., Poli, R.: Fitness causes bloat: Mutation. In: Koza, J. (ed.) Late Breaking Papers at GP 1997, Stanford Bookstore, pp. 132–140 (1997)

    Google Scholar 

  13. Langdon, W.B., Poli, R.: Foundations of Genetic Programming. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  14. Langdon, W.B., Soule, T., Poli, R., Foster, J.A.: The evolution of size and shape. In: Spector, L., Langdon, W.B., O’Reilly, U.-M., Angeline, P. (eds.) Advances in Genetic Programming III, pp. 163–190. MIT Press, Cambridge (1999)

    Google Scholar 

  15. Langdon, W.B.: Genetic Programming and Data Structures: Genetic Programming + Data Structures = Automatic Programming!, April 24, 1998. Genetic Programming, vol. 1. Kluwer, Boston (1998)

    Google Scholar 

  16. Luke, S., Panait, L.: Lexicographic parsimony pressure. In: Langdon, W.B., et al. (eds.) GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 829–836. Morgan Kaufmann Publishers, San Francisco (2002)

    Google Scholar 

  17. Nordin, P., Banzhaf, W.: Complexity compression and evolution. In: Eshelman, L. (ed.) Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA 1995), Pittsburgh, PA, USA, July 15-19, 1995, pp. 310–317. Morgan Kaufmann, San Francisco (1995)

    Google Scholar 

  18. Pareto, V.: Manuale d’Economia Politica. Società Editrice, Libraria, Milano (1906)

    Google Scholar 

  19. Ratle, A., Sebag, M.: Avoiding the bloat with probabilistic grammar-guided genetic programming. In: Collet, P., Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M. (eds.) EA 2001. LNCS, vol. 2310, Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Rogers, H.: Theory of recursive functions and effective computability. McGraw-Hill, New York (1967)

    MATH  Google Scholar 

  21. Schmidthuber, J.: Hierarchies of generalized kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science 13(4), 587–612 (2002)

    Article  MathSciNet  Google Scholar 

  22. Silva, S., Almeida, J.: Dynamic maximum tree depth: A simple technique for avoiding bloat in tree-based gp. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1776–1787. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  23. Sipser, M.: A complexity theoretic approach to randomness. In: Proceedings of the 15th ACM Symposium on the Theory of Computing, pp. 330–335. ACM Press, New York (1983)

    Google Scholar 

  24. Solomonoff, R.: A formal theory of inductive inference, part 1. Inform. and Control 7(1), 1–22 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  25. Solomonoff, R.: A formal theory of inductive inference, part 2. Inform. and Control 7(2), 222–254 (1964)

    Article  Google Scholar 

  26. Soule, T., Foster, J.A.: Effects of code growth and parsimony pressure on populations in genetic programming. Evolutionary Computation 6(4), 293–309 (1998)

    Article  Google Scholar 

  27. Soule, T.: Exons and code growth in genetic programming. In: Foster, J.A., Lutton, E., Miller, J., Ryan, C., Tettamanzi, A.G.B. (eds.) EuroGP 2002. LNCS, vol. 2278, pp. 142–151. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  28. Turing, A.: On computable numbers, with an application to the entscheidungsproblem. In: Proceedings of the London Mathematical Society, vol. 2, 45, pp. 161–228 (reprinted in Davis, M.: The Undecidable, pp. 155-222, Raven Press, Ewlett, NY (1965)) (1936-1937)

    Google Scholar 

  29. Vapnik, V.: The nature of statistical learning. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  30. Zhang, B.-T., Muhlenbein, H.: Balancing accuracy and parsimony in genetic programming. Evolutionary Computation 3(1), 17–38 (1995)

    Article  Google Scholar 

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Jérôme Durand-Lose Maurice Margenstern

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Teytaud, O. (2007). Slightly Beyond Turing’s Computability for Studying Genetic Programming. In: Durand-Lose, J., Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2007. Lecture Notes in Computer Science, vol 4664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74593-8_24

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  • DOI: https://doi.org/10.1007/978-3-540-74593-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74592-1

  • Online ISBN: 978-3-540-74593-8

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