Abstract
Theoretical models of Turing complete linear genetic programming (GP) programs suggest the fraction of halting programs is vanishingly small. Convergence results proved for an idealised machine, are tested on a small T7 computer with (finite) memory, conditional branches and jumps. Simulations confirm Turing complete fitness landscapes of this type hold at most a vanishingly small fraction of usable solutions.
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Langdon, W.B., Poli, R.: Foundations of Genetic Programming (2002)
McPhee, N.F., Poli, R.: Using schema theory to explore interactions of multiple operators. In: Langdon, W.B., et al. (eds.) GECCO 2002, pp. 853–860 (2002)
Rosca, J.: A probabilistic model of size drift. In: Riolo, R.L., Worzel, B. (eds.) Genetic Programming Theory and Practice, pp. 119–136. Kluwer, Dordrecht (2003)
Sastry, K., O’Reilly, U.-M., Goldberg, D.E., Hill, D.: Building block supply GP. In: Genetic Programming Theory and Practice, pp. 137–154. Kluwer, Dordrecht (2003)
Mitavskiy, B., Rowe, J.E.: A schema-based version of Geiringer’s theorem for nonlinear genetic programming with homologous crossover. In: Wright, A.H., Vose, M.D., De Jong, K.A., Schmitt, L.M. (eds.) FOGA 2005. LNCS, vol. 3469, pp. 156–175. Springer, Heidelberg (2005)
Daida, J.M., Hilss, A.M., Ward, D.J., Long, S.L.: Visualizing tree structures in genetic programming. Genetic Programming and Evolvable Machines 6(1), 79–110
Langdon, W.B.: Convergence rates for the distribution of program outputs. In: Langdon, W.B., et al. (eds.) GECCO 2002, New York, July 9-13, pp. 812–819 (2002)
Langdon, W.B.: How many good programs are there? How long are they? In: De Jong, K.A., et al. (eds.) FOGA 7, pp. 183–202. Morgan Kaufmann. Published, San Francisco (2003)
Langdon, W.B.: The distribution of reversible functions is Normal. In: Genetic Programming Theory and Practise, pp. 173–188. Kluwer Academic Publishers, Dordrecht (2003)
Langdon, W.B.: Convergence of program fitness landscapes. 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. 1702–1714. Springer, Heidelberg (2003)
Teller, A.: Turing completeness in the language of GP with indexed memory. In: 1994 IEEE World Congress on Computational Intelligence, pp. 136–141 (1994)
Langdon, W.B.: Quadratic bloat in genetic programming. In: Whitley, D., et al. (eds.) GECCO 2000, pp. 451–458 (2000)
Langdon, W.B., Poli, R.: On Turing complete T7 and MISC F-4 program fitness landscapes. Technical Report CSM-445, University of Essex, UK (2005)
Maxwell III, S.R.: Experiments with a coroutine model for genetic programming. In: 1994 IEEE World Congress on Computational Intelligence, pp. 413–417a (1994)
Chaitin, G.J.: An algebraic equation for the halting probability. In: R. Herken, ed., The Universal Turing Machine A Half-Century Survey, pp. 279–283. OUP (1988)
Calude, C.S., Dinneen, M.J., Shu, C.-K.: Computing a glimpse of randomness. Experimental Mathematics 11(3), 361–370 (2002)
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Langdon, W.B., Poli, R. (2006). The Halting Probability in Von Neumann Architectures. In: Collet, P., Tomassini, M., Ebner, M., Gustafson, S., Ekárt, A. (eds) Genetic Programming. EuroGP 2006. Lecture Notes in Computer Science, vol 3905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11729976_20
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DOI: https://doi.org/10.1007/11729976_20
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