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Area of Science:

  • Cognitive Psychology
  • Computer Science
  • Information Theory

Background:

  • Assessing executive functions, particularly inhibition, increasingly relies on analyzing human-produced random sequences.
  • Existing measures of randomness are limited, focusing on single features and requiring multiple assessments.
  • Algorithmic complexity offers a unified measure but standard Kolmogorov complexity is unsuitable for short strings.

Purpose of the Study:

  • To introduce a novel, objective, and universal method for measuring algorithmic complexity in short strings.
  • To address the limitations of existing randomness measures in cognitive assessments.
  • To approximate Kolmogorov-Chaitin complexity for short sequences.

Main Methods:

  • Development of the coding theorem method.
  • Calculation of a universal distribution.
  • Application to short strings (length ≤ 50).

Main Results:

  • The coding theorem method provides an objective and universal measure of algorithmic complexity for short strings.
  • This technique overcomes the computational and theoretical limitations of standard Kolmogorov complexity.
  • The method approximates Kolmogorov-Chaitin complexity.

Conclusions:

  • The coding theorem method offers a practical solution for assessing algorithmic complexity in short sequences.
  • This advancement can improve the assessment of executive functions through randomness production analysis.
  • A single, objective measure of randomness is now feasible for short strings.