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Dynamics and Complexity of Computrons.

Murat Erkurt1

  • 1Department of Mathematics, Centre for Complexity Science, Imperial College London, South Kensington campus, London SW7 2AZ, UK.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

We introduce computrons, generalized automata with complex network rules and external inputs. New metrics quantify their chaotic dynamics and state space complexity, offering insights into computation and complex systems.

Keywords:
cellular automatacomplexitycomputrondiversity measureentanglementgeneral network automata

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Area of Science:

  • Complex Systems
  • Theoretical Computer Science
  • Dynamical Systems

Background:

  • Cellular automata (CA) are fundamental models for complex systems.
  • Existing CA models often lack flexibility in rules, connectivity, and external inputs.
  • Understanding chaoticity and complexity in computational models is crucial.

Purpose of the Study:

  • To introduce and define 'computrons' as a generalization of CA.
  • To develop novel set-theoretic concepts for analyzing computron dynamics.
  • To quantify chaoticity and complexity in these generalized automata.

Main Methods:

  • Representing finite-state machines as computrons.
  • Defining 'diversity space' as a metric space for configuration similarity.
  • Defining 'basin complexity' to measure partition complexity of the diversity space.
  • Extending theory to probabilistic machines with fuzzy basin partitioning and ergodic decomposition.

Main Results:

  • Demonstrated that any finite-state machine can be represented as a computron.
  • Introduced quantifiable measures for chaoticity and basin complexity.
  • Developed a framework for analyzing probabilistic computrons, including ergodic decomposition.
  • Presented a case study on 1D cyclic computrons.

Conclusions:

  • Computrons offer a flexible and powerful framework for modeling complex computational systems.
  • The developed metrics provide novel ways to quantify chaotic dynamics and state space complexity.
  • The theory extends to probabilistic settings, enhancing the applicability to real-world systems.