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":
... 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 ... 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 ...
... 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 ...
Famous quotes containing the words thickness and/or finite:
“For his teeth seem for laughing round an apple.
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Nor antlers through the thickness of his curls.”
—Wilfred Owen (1893–1918)
“Put shortly, these are the two views, then. One, that man is intrinsically good, spoilt by circumstance; and the other that he is intrinsically limited, but disciplined by order and tradition to something fairly decent. To the one party man’s nature is like a well, to the other like a bucket. The view which regards him like a well, a reservoir full of possibilities, I call the romantic; the one which regards him as a very finite and fixed creature, I call the classical.”
—Thomas Ernest Hulme (1883–1917)