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 ).
Famous quotes containing the words finite and/or thickness:
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“For his teeth seem for laughing round an apple.
There lurk no claws behind his fingers supple;
And God will grow no talons at his heels,
Nor antlers through the thickness of his curls.”
—Wilfred Owen (1893–1918)