Typology of Boolean Functions Using Walsh Analysis

  • Cathy Escazut
  • Philippe Collard
Conference paper


Much previous works deal with the functions that cause a genetic algorithm (GA) to diverge from the global optimum. It is now a fact: Walsh analysis allows the identification of GA-hard problems. But what about genetics-based machine learning? Do we know what makes a problem hard for a classifier system (CS)? In order to try to answer these questions, we describe the relation between CS performance and the structure of a given boolean function when it is expressed as a Walsh polynomial. The analysis of the relative magnitude of Walsh coefficients allows us to set up a typology of boolean functions according to their hardness for a CS. Thus, each function can be placed in a specific class of difficulty. Using the converse process, we can start from well chosen Walsh coefficients in order to build boolean functions hard for a CS to learn.


Genetic Algorithm Boolean Function Classifier System Truth Table Input String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. D. Bethke. Genetic algorithms as function optimizers. PhD thesis, University of Michigan, 1980.Google Scholar
  2. [2]
    D. E. Goldberg. Genetic algorithms and walsh functions. Complex Systems, 3:pp 129–171, 1989.MathSciNetMATHGoogle Scholar
  3. [3]
    D. E. Goldberg. Construction of high-order deceptive functions using low-order walsh coefficients. Annals of Mathematics and Artificial Intelligence, 5:pp 35–48, 1992.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    J. H. Holland. Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press, 1975.Google Scholar
  5. [5]
    J. R. Koza. Genetic programming: On the programming of computers by means of natural selection. MIT Press, Cambridge, MA, 1993.Google Scholar
  6. [6]
    S. W. Wilson. Classifier systems and the animat problem. Machine Learning, 2 (3): 199–218, 1987.Google Scholar

Copyright information

© Springer-Verlag/Wien 1995

Authors and Affiliations

  • Cathy Escazut
    • 1
  • Philippe Collard
    • 1
  1. 1.Laboratory I3S — CNRS-UNSAValbonneFrance

Personalised recommendations