Natural Computing

, Volume 7, Issue 1, pp 21–43 | Cite as

Mapping non-conventional extensions of genetic programming

Article
  • 79 Downloads

Abstract

Conventional genetic programming research excludes memory and iteration. We have begun an extensive analysis of the space through which GP or other unconventional AI approaches search and extend it to consider explicit program stop instructions (T8), including Markov analysis and any time models (T7). We report halting probability, run time and functionality (including entropy of binary functions) of both halting and anytime programs. Irreversible Turing complete program fitness landscapes, even with halt, scale poorly however loops lock-in variation allowing more interesting functions.

Keywords

Turing complete Markov analysis of program search spaces Program termination Any time computation Entropy and irreversible loss of information Program convergence Halting probability genetic algorithms Genetic programming 

Notes

Acknowledgements

We would like to thank Dagstuhl Seminar 06061.

References

  1. Banzhaf W, Nordin P, Keller RE, Francone FD (1998) Genetic programming—an introduction; On the automatic evolution of computer programs and its applications. Morgan Kaufmann, San Francisco, CA, USAGoogle Scholar
  2. Daida JM, Bertram RR, Polito JA 2, Stanhope SA (1999) Analysis of single-node (building) blocks in genetic programming. In: Spector L, Langdon WB, O’Reilly U-M, Angeline PJ (eds) Advances in genetic programming 3, chapter 10. MIT Press, Cambridge, MA, USA, pp 217–241Google Scholar
  3. Greene WA (2004) Greene. Schema disruption in chromosomes that are structured as binary trees. In: Deb K et al. (eds) Genetic and evolutionary computation—GECCO-2004, Part I, vol 3102 of Lecture Notes in Computer Science. Springer-Verlag, Seattle, WA, USA, pp 1197–1207Google Scholar
  4. Langdon WB (2002) Convergence rates for the distribution of program outputs. In: Langdon WB et al. (eds) GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference. New York, July 2002, pp 812–819Google Scholar
  5. Langdon WB (2003a) How many good programs are there? How long are they? In: De Jong KA, Poli R, Rowe JE (eds) Foundations of genetic algorithms VII. Torremolinos, Spain, 4–6 September 2002. Morgan Kaufmann, pp 183–202Google Scholar
  6. Langdon WB (2003b) The distribution of reversible functions is Normal. In: Riolo RL, Worzel B (eds) Genetic programming theory and practice, chapter 11. Kluwer, pp 173–188Google Scholar
  7. Langdon WB (2003c) Convergence of program fitness landscapes. In: Cantú-Paz E et al. (eds) Genetic and evolutionary computation—GECCO-2003, vol 2724 of LNCS, Chicago, 12–16 July 2003. Springer-Verlag, pp 1702–1714Google Scholar
  8. Langdon WB (2006) Mapping non-conventional extensions of genetic programming. In: Calude CS, Dinneen MJ, Paun G, Rozenberg G, Stepney S (eds) Unconventional computing 2006, vol 4135 of LNCS, York. Springer-Verlag, pp 166–180Google Scholar
  9. Langdon WB, Poli R (2002) Foundations of genetic programming. Springer-VerlagGoogle Scholar
  10. Langdon WB, Poli R (2005) On turing complete T7 and MISC F-4 program fitness landscapes. Technical Report CSM-445, Computer Science, University of Essex, UKGoogle Scholar
  11. Langdon WB, Poli R (2006) The halting probability in von Neumann architectures. In: Collet P et al. (eds) Proceedings of the 9th European Conference on Genetic Programming, vol 3905 of Lecture Notes in Computer Science, pp 225–237, Budapest, Hungary, 10–12 April 2006, SpringerGoogle Scholar
  12. Maxwell SR III (1994) Experiments with a coroutine model for genetic programming. In: Proceedings of the 1994 IEEE World Congress on Computational Intelligence. Orlando, Florida, USA, 27–29 June 1994. IEEE, pp 413a–417aGoogle Scholar
  13. McPhee NF, Poli R (2002) Using schema theory to explore interactions of multiple operators. In: Langdon WB et al. (eds) GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, New York, July 2002. Morgan Kaufmann, pp 853, 860Google Scholar
  14. Poli R, Langdon WB (2006) Efficient markov chain model of machine code program execution and halting. In: Riolo RL, Soule T, Worzel B (eds) Genetic programming theory and practice IV, vol 5 of Genetic and evolutionary computation. Springer, Ann ArborGoogle Scholar
  15. Rosca J (2003) A probabilistic model of size drift. In: Riolo RL, Worzel B (eds) Genetic programming theory and practice. Kluwer Academic Publishers, pp 119–136Google Scholar
  16. Sastry K, O’Reilly U-M, Goldberg DE, Hill D (2003) Building block supply in genetic programming. In: Riolo RL, Worzel B (eds) Genetic programming theory and practice. Kluwer, pp 137–154Google Scholar
  17. Shannon CE, Weaver W (1964) The mathematical theory of communication. The University of Illinois Press, UrbanaGoogle Scholar
  18. Spector L, Klein J, Keijzer M (2005) The push3 execution stack and the evolution of control. In: Beyer H-G et al (eds) GECCO 2005: Proceedings of the 2005 conference on Genetic and evolutionary computation, vol 2, Washington DC, USA, 25–29 June 2005. ACM Press, pp 1689–1696Google Scholar
  19. Teller A (1994) Genetic programming, indexed memory, the halting problem, and other curiosities. In Proceedings of the 7th annual Florida Artificial Intelligence Research Symposium, Pensacola, Florida, USA. IEEE, pp 270–274Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of EssexColchesterUK
  2. 2.Department of Computer ScienceUniversity of EssexColchesterUK

Personalised recommendations