# Scaling of Program Functionality

Created by W.Langdon from gp-bibliography.bib Revision:1.4031

@Article{langdon:2007:gpem,
author =       "W. B. Langdon",
title =        "Scaling of Program Functionality",
journal =      "Genetic Programming and Evolvable Machines",
year =         "2009",
volume =       "10",
number =       "1",
pages =        "5--36",
month =        mar,
keywords =     "genetic algorithms, genetic programming, search
landscapes, evolutionary computation",
ISSN =         "1389-2576",
URL =          "http://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/papers/wbl_scale_prog_func.pdf",
DOI =          "doi:10.1007/s10710-008-9065-y",
size =         "32 pages",
abstract =     "The distribution of fitness values (landscapes) of
programs tends to a limit as the programs get bigger.
We use Markov chain convergence theorems to give
general upper bounds on the length of programs needed
for convergence. How big programs need to be to
approach the limit depends on the type of the computer
they run on. We give bounds (exponential in $N$, $N\log N$ and smaller) for five computer models: any, average
or amorphous or random, cyclic, bit flip and 4
functions (AND, NAND, OR and NOR).

Programs can be treated as lookup tables which map
between their inputs and their outputs. Using this we
prove similar convergence results for the distribution
of functions implemented by linear computer programs.
We show most functions are constants and the remainder
are mostly parsimonious.

The effect of ad-hoc rules on genetic programming (GP)
are described and new heuristics are proposed.

We give bounds on how long programs need to be before
the distribution of their functionality is close to its
limiting distribution, both in general and for average
computers. The computational importance of destroying
information is discussed with respect to reversible and
quantum computers.

Mutation randomizes a genetic algorithm population in
\frac{1}{4}(l+1)(\log(l)+4) generations.

Results for average computers and a model like genetic
programming are confirmed experimentally.",
}



Genetic Programming entries for William B Langdon

Citations