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Algorithmic complexity for psychology: a user-friendly implementation of the coding theorem method.

Nicolas Gauvrit1, Henrik Singmann2, Fernando Soler-Toscano3

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Summary
This summary is machine-generated.

Algorithmic complexity for short strings (ACSS) can now be estimated using a new coding theorem method. This R-package offers improved, faster calculations for psychologists, applicable to strings of any length.

Keywords:
Algorithmic complexityCoding theorem methodRandomnessSubjective probability

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Area of Science:

  • Computational complexity theory
  • Psychological measurement
  • Information theory

Background:

  • Kolmogorov-Chaitin complexity is crucial for understanding randomness and information.
  • Approximating complexity for short sequences has been a significant computational challenge.
  • Previous methods were limited in scope and computational efficiency.

Purpose of the Study:

  • To introduce the theoretical basis of Algorithmic Complexity for Short Strings (ACSS).
  • To present an R-package implementing ACSS for practical psychological research.
  • To enhance the estimation of algorithmic complexity for short and long strings.

Main Methods:

  • Development of the coding theorem method for complexity estimation.
  • Implementation of ACSS in a user-friendly R-package.
  • Extension of ACSS to strings with up to 9 symbols and improved computational speed.

Main Results:

  • Numerical estimation of complexity is now feasible for strings of length 2-11.
  • ACSS provides a faster and more versatile alternative to previous complexity approximation methods.
  • A novel approach allows for the estimation of complexity for strings of any length.

Conclusions:

  • The ACSS R-package offers significant advancements for psychological research requiring complexity analysis.
  • The new method overcomes previous limitations in computational time and symbol set size.
  • This work provides accessible tools for quantifying string complexity in various psychological applications.