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Related Experiment Video

Updated: May 21, 2026

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

Computability-theoretic learning complexity.

John Case1, Timo Kötzing

  • 1Department of Computer and Information Sciences, University of Delaware, Newark, 19716-2586, USA. case@cis.udel.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 20, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces epitomizing sets as a new way to analyze function learnability in computability theory, overcoming limitations of intrinsic complexity. New reducibility notions help characterize these sets, leading to easier identification and generation of strong epitomizers.

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Area of Science:

  • Computability-theoretic learning theory
  • Theoretical computer science
  • Algorithmic learning theory

Background:

  • Explores Alan Turing's ideas on mind and mechanism.
  • Focuses on algorithmic, trial-and-error program inference from data points.
  • Critiques the use of intrinsic complexity in analyzing function learnability within Gold-style learning settings.

Purpose of the Study:

  • Introduce epitomizing sets as an alternative to intrinsic complexity for analyzing learning complexity.
  • Develop new reducibility notions based on robust learning to capture the concept of epitomizing sets.
  • Characterize degrees of epitomizing sets and provide methods for their identification and generation.

Main Methods:

  • Introduced new reducibility notions based on robust learning.
  • Characterized various degrees of epitomizing sets using these new notions.
  • Employed these characterizations to prove sets as epitomizers and developed a scheme for generating strong epitomizers (self-learning sets).

Main Results:

  • Identified weaknesses in the notion of intrinsic complexity.
  • Defined epitomizing sets as learnable under a criterion but not under weaker ones.
  • Characterized epitomizing sets as complete with respect to new reducibility notions.
  • Provided a scheme for generating strong epitomizers, specifically self-learning sets.

Conclusions:

  • Epitomizing sets offer a robust alternative for analyzing learning complexity.
  • New reducibility notions provide effective tools for characterizing and identifying epitomizing sets.
  • The developed scheme facilitates the generation of strong epitomizers, demonstrating strict separations in learning power between criteria.