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McCulloch-Pitts Brains and Pseudorandom Functions.

Vašek Chvátal1, Mark Goldsmith2, Nan Yang3

  • 1Department of Computer Science and Software Engineering, Concordia University, Montreal, QC H3G 1M8, Canada chvatal@cse.concordia.ca.

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Central nervous system models cannot generate unpredictable outputs. Researchers demonstrate that engineered dynamical systems, inspired by brain activity, are incapable of producing weak pseudorandom functions, limiting their unpredictability.

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Area of Science:

  • Computational neuroscience
  • Theoretical computer science
  • Dynamical systems theory

Background:

  • The McCulloch-Pitts model provided an early framework for understanding the central nervous system.
  • Electroencephalography (EEG) recordings reveal complex, dynamic patterns in normal brain activity.
  • The question arises whether these biological systems can be engineered for unpredictable behavior.

Purpose of the Study:

  • To investigate the inherent limitations of engineered dynamical systems in generating pseudorandomness.
  • To determine if models of the central nervous system can produce irregular and unpredictable trajectories.
  • To analyze the capabilities of these systems in constructing weak pseudorandom functions.

Main Methods:

  • Analysis of dynamical systems based on the McCulloch-Pitts model.
  • Theoretical examination of function generation within these systems.
  • Mathematical proofs to establish the impossibility of creating weak pseudorandom functions.

Main Results:

  • Engineered dynamical systems, inspired by neural activity, cannot produce weak pseudorandom functions.
  • The inherent structure of these models limits their capacity for generating true unpredictability.
  • Trajectories generated by these systems exhibit predictable patterns rather than randomness.

Conclusions:

  • The study reveals fundamental constraints on the unpredictability of engineered neural models.
  • It is not possible to engineer systems based on the McCulloch-Pitts model to generate weak pseudorandom functions.
  • This finding has implications for understanding the limits of artificial neural systems and biological computation.