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Finite statistical complexity for sofic systems.

N Perry1, P M Binder

  • 1Departamento de Física, Universidad de Los Andes, Apartado Aéreo 4976, Bogotá, Colombia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
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We introduce a new computational complexity measure for symbolic sequences using conditional probabilities. This method identifies causal states in dynamical systems without needing complex automata construction.

Area of Science:

  • Complexity Science
  • Dynamical Systems Theory
  • Information Theory

Background:

  • Assessing the computational complexity of symbolic sequences is crucial for understanding complex systems.
  • Traditional methods often rely on constructing minimal deterministic finite automata (DFA), which can be computationally intensive.
  • Dynamical systems generate sequences that require robust methods for complexity analysis.

Purpose of the Study:

  • To propose a novel measure of complexity for symbolic sequences based on conditional probabilities.
  • To capture computational complexity without explicit minimal deterministic finite automata (DFA) construction.
  • To identify and estimate causal states in dynamical systems from their encoded sequences.

Main Methods:

  • Developed a complexity measure leveraging conditional probabilities of symbol occurrences.

Related Experiment Videos

  • Applied the measure to symbolic sequences derived from dynamical systems via suitable encoding.
  • Utilized known equations of motion to estimate phase space regions corresponding to causal states.

    • Main Results:

    • The proposed measure effectively quantifies computational complexity.
    • Successfully estimated causal states, representing regions with statistically equivalent futures.
    • Demonstrated the method's efficacy without requiring explicit minimal DFA construction.

    Conclusions:

    • The conditional probability-based complexity measure offers an efficient alternative for analyzing symbolic sequences.
    • This approach facilitates the understanding of computational states within dynamical systems.
    • The method provides a pathway to link dynamical system properties to computational complexity.