A Family of Gödel Machine Implementations

  • Bas R. Steunebrink
  • Jürgen Schmidhuber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6830)


The Gödel Machine is a universal problem solver encoded as a completely self-referential program capable of rewriting any part of itself, provided it can prove that the rewrite is useful according to some utility function, encoded within itself. Based on experience gained by constructing a virtual machine capable of running the first Gödel Machine implementation written in self-referential code, we discuss several important refinements of the original concept. We also show how different approaches to implementing the proof search leads to a family of possible Gödel Machine implementations.


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  1. 1.
    Abelson, H., Sussman, G.J., Sussman, J.: Structure and Interpretation of Computer Programs, 2nd edn. MIT Press, Cambridge (1996)zbMATHGoogle Scholar
  2. 2.
    Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik 38, 173–198 (1931)CrossRefGoogle Scholar
  3. 3.
    Hutter, M.: The fastest and shortest algorithm for all well-defined problems. International Journal of Foundations of Computer Science 13(3), 431–443 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Jefferson, S., Friedman, D.P.: A simple reflective interpreter. LISP and Symbolic Computation 9(2-3), 181–202 (1996)CrossRefGoogle Scholar
  5. 5.
    Kelsey, R., Clinger, W., Rees, J. (eds.): Revised5 report on the algorithmic language Scheme. Higher-Order and Symbolic Computation 11(1) (August 1998)Google Scholar
  6. 6.
    Queinnec, C.: Lisp in Small Pieces. Cambridge University Press, Cambridge (1996)zbMATHGoogle Scholar
  7. 7.
    Schmidhuber, J.: Completely self-referential optimal reinforcement learners. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 223–233. Springer, Heidelberg (2005)Google Scholar
  8. 8.
    Schmidhuber, J.: Gödel machines: Fully self-referential optimal universal self-improvers. In: Goertzel, B., Pennachin, C. (eds.) Artificial General Intelligence, pp. 199–226. Springer Verlag (2006); variant available as arXiv:cs.LO/0309048Google Scholar
  9. 9.
    Schmidhuber, J.: Ultimate cognition à la Gödel. Cognitive Computation 1(2), 177–193 (2009)CrossRefGoogle Scholar
  10. 10.
    Schmidhuber, J.: Gödel machines: Self-referential universal problem solvers making provably optimal self-improvements. Tech. Rep. IDSIA-19-03, arXiv:cs.LO/0309048 v2, IDSIA (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bas R. Steunebrink
    • 1
  • Jürgen Schmidhuber
    • 1
  1. 1.IDSIA & University of LuganoSwitzerland

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