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.