Language Identification in The Limit - Relations Between Concepts

Relations Between Concepts

  • Finite thickness implies finite elasticity; the converse is not true.
  • Finite elasticity and conservatively learnable implies the existence of a mind change bound.
  • Finite elasticity and M-finite thickness implies the existence of a mind change bound. However, M-finite thickness alone does not imply the existence of a mind change bound; neither does the existence of a mind change bound imply M-finite thickness.
  • Existence of a mind change bound implies learnability; the converse is not true.
  • If we allow for noncomputable learners, then finite elasticity implies the existence of a mind change bound; the converse is not true.
  • If there is no accumulation order for a class of languages, then there is a language (not necessarily in the class) that has infinite cross property within the class, which in turn implies infinite elasticity of the class.

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