Finite Thickness

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In formal language theory, a class of languages has finite thickness if for every string s, there are only finitely many consistent languages in . This condition was introduced by Dana Angluin in connection with learning, as a sufficient condition for language identification in the limit. The related notion of M-finite thickness

We say that satisfies the MEF-condition if for each string s and each consistent language L in the class, there is a minimal consistent language in, which is a sublanguage of L. Symmetrically, we say that satisfies the MFF-condition if for every string s there are only finitely many minimal consistent languages in . Finally, is said to have M-finite thickness if it satisfies both the MEF and MFF conditions.

Finite thickness implies M-finite thickness. However, there are classes that are of M-finite thickness but not of finite thickness (for example, let be a class of languages such that ).

Other articles related to "finite thickness, finite":

Language Identification In The Limit - 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 ... 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 ...
Language Identification In The Limit - Sufficient Conditions For Learnability - Finite Thickness
... A class of languages has finite thickness if for every string s, there are only a finite number of languages in the class that are consistent with s ... Angluin showed that if a class of recursive languages has finite thickness, then it is learnable in the limit ... A class with finite thickness certainly satisfies MEF-condition and MFF-condition in other words, finite thickness implies M-finite thickness ...

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