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:
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)
“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)