Behavior Research Methods

, Volume 46, Issue 3, pp 732–744

Algorithmic complexity for short binary strings applied to psychology: a primer

  • Nicolas Gauvrit
  • Hector Zenil
  • Jean-Paul Delahaye
  • Fernando Soler-Toscano
Article

DOI: 10.3758/s13428-013-0416-0

Cite this article as:
Gauvrit, N., Zenil, H., Delahaye, JP. et al. Behav Res (2014) 46: 732. doi:10.3758/s13428-013-0416-0

Abstract

As human randomness production has come to be more closely studied and used to assess executive functions (especially inhibition), many normative measures for assessing the degree to which a sequence is randomlike have been suggested. However, each of these measures focuses on one feature of randomness, leading researchers to have to use multiple measures. Although algorithmic complexity has been suggested as a means for overcoming this inconvenience, it has never been used, because standard Kolmogorov complexity is inapplicable to short strings (e.g., of length l ≤ 50), due to both computational and theoretical limitations. Here, we describe a novel technique (the coding theorem method) based on the calculation of a universal distribution, which yields an objective and universal measure of algorithmic complexity for short strings that approximates Kolmogorov–Chaitin complexity.

Keywords

Algorithmic complexity Randomness Subjective probability 

Copyright information

© Psychonomic Society, Inc. 2013

Authors and Affiliations

  • Nicolas Gauvrit
    • 1
  • Hector Zenil
    • 2
  • Jean-Paul Delahaye
    • 3
  • Fernando Soler-Toscano
    • 4
  1. 1.CHART (PARIS-reasoning)University of Paris VIII and EPHEParisFrance
  2. 2.Unit of Computational Medicine, Center for Molecular MedicineKarolinska InstituteStockholmSweden
  3. 3.Laboratoire d’Informatique Fondamentale de LilleLilleFrance
  4. 4.Grupo de Lógica, Lenguaje e InformaciónUniversidad de SevillaSevilleSpain