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Enumerating Finitary Processes.

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  • 1Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study presents an efficient method for enumerating finite-memory stochastic processes using epsilon-machines. The approach adapts automata theory algorithms to precisely count these complex systems.

Keywords:
epsilon-machineorderly enumeration

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Area of Science:

  • Theoretical Computer Science
  • Information Theory
  • Dynamical Systems

Background:

  • Stochastic processes are fundamental to modeling complex systems.
  • Finite-memory processes are a key subclass, but efficient enumeration remains challenging.
  • Epsilon-machines offer a causal framework for representing these processes.

Purpose of the Study:

  • To develop an efficient method for enumerating finite-memory stochastic processes.
  • To characterize epsilon-machines within automata theory.
  • To apply this framework to enumerate specific classes of epsilon-machines.

Main Methods:

  • Utilizing the causal representation of epsilon-machines.
  • Adapting algorithms for generating accessible deterministic finite automata.
  • Pruning the set of deterministic finite automata to identify epsilon-machines.
  • Applying the method to enumerate topological epsilon-machines.

Main Results:

  • An efficient algorithm for enumerating epsilon-machines is presented.
  • Epsilon-machines are formally characterized using automata theory.
  • The method successfully enumerates topological epsilon-machines up to eight states and six-letter alphabets.

Conclusions:

  • The developed method provides an efficient means to enumerate finite-memory stochastic processes.
  • This work bridges theoretical computer science and the study of complex systems.
  • The enumeration results offer a foundation for further analysis of stochastic process complexity.